finding a tangent line to a parabola Unicorn Meta Zoo #1: Why another podcast? ...
Align column where each cell has two decimals with siunitx
How to get even lighting when using flash for group photos near wall?
Arriving in Atlanta after US Preclearance in Dublin. Will I go through TSA security in Atlanta to transfer to a connecting flight?
Israeli soda type drink
Suing a Police Officer Instead of the Police Department
What do you call the part of a novel that is not dialog?
What is the ongoing value of the Kanban board to the developers as opposed to management
What is the least dense liquid under normal conditions?
What is it called when you ride around on your front wheel?
The art of proof summarizing. Are there known rules, or is it a purely common sense matter?
My bank got bought out, am I now going to have to start filing tax returns in a different state?
Justification for leaving new position after a short time
Multiple options vs single option UI
Did the Roman Empire have penal colonies?
PIC mathematical operations weird problem
How to use @AuraEnabled base class method in Lightning Component?
Married in secret, can marital status in passport be changed at a later date?
Why did C use the -> operator instead of reusing the . operator?
How long after the last departure shall the airport stay open for an emergency return?
AI positioning circles within an arc at equal distances and heights
Multiple fireplaces in an apartment building?
c++ diamond problem - How to call base method only once
What *exactly* is electrical current, voltage, and resistance?
Mistake in years of experience in resume?
finding a tangent line to a parabola
Unicorn Meta Zoo #1: Why another podcast?
Announcing the arrival of Valued Associate #679: Cesar ManaraHow do I find the equation of a tangent line to a curve?Find intersection(s) between parametrized parabola and a lineHow to find equation of tangent line to $x^2 = 2y$ at $(-3, 9/2)$Find the equation of parabola tangent to a lineWhy is this answer wrong? (point of intersection between parabola and line)Euclid 1999 Question 4(a) - Circle Tangent Intersection4 tangent lines to parabola with points on circleFinding the Equation for the Line Tangent to a Parabola At a Given PointMirror image of the parabola about a tangentMaximizing $x^2 y + y^2 z + z^2 x − x^2 z − y^2 x − z^2 y$ for $x$, $y$, $z$ between $0$ and $1$ (inclusive)Find the numerical value of this expression
$begingroup$
I am practicing for a math contest and I encountered the following problem that I don't know how to solve:
For which value of $b$ is there only one intersection between the line $y = x + b$ and the parabola $y = x^2 + 5x + 3$?
How do I solve it?
algebra-precalculus contest-math
edited 2 hours ago
NoChance
3,79221321
asked 2 hours ago
swagbutton8swagbutton8
61
New contributor
swagbutton8 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
I am practicing for a math contest and I encountered the following problem that I don't know how to solve:
For which value of $b$ is there only one intersection between the line $y = x + b$ and the parabola $y = x^2 + 5x + 3$?
How do I solve it?
algebra-precalculus contest-math
edited 2 hours ago
NoChance
3,79221321
asked 2 hours ago
swagbutton8swagbutton8
61
New contributor
swagbutton8 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
1
$begingroup$
Do you know how to find a derivative?
$endgroup$
– R. Burton
2 hours ago
$begingroup$
Simply $x^2+5x+3=x+b$ must have only one solution, i.e. $x^2+4x+(3-b)=0$ should have zero discriminant.
$endgroup$
– the_fox
2 hours ago
$begingroup$
A Parabola could have many tangent lines...However, it has only 1 min. value, may be this one is the one you are after. More here:desmos.com/calculator/zz7e1nwgf9 and here:info:math.stackexchange.com/questions/92165/…
$endgroup$
– NoChance
1 hour ago
1
$begingroup$
@NoChance Your observation would be relevant if the line’s equation were of the form $y=b$. The line in the problem is not horizontal, though.
$endgroup$
– amd
42 mins ago
$begingroup$
@amd, thanks for your comment. I am not sure which tangent line one should pick then?
$endgroup$
– NoChance
10 mins ago
add a comment |
$begingroup$
I am practicing for a math contest and I encountered the following problem that I don't know how to solve:
For which value of $b$ is there only one intersection between the line $y = x + b$ and the parabola $y = x^2 + 5x + 3$?
How do I solve it?
algebra-precalculus contest-math
edited 2 hours ago
NoChance
3,79221321
asked 2 hours ago
swagbutton8swagbutton8
61
New contributor
swagbutton8 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
I am practicing for a math contest and I encountered the following problem that I don't know how to solve:
For which value of $b$ is there only one intersection between the line $y = x + b$ and the parabola $y = x^2 + 5x + 3$?
How do I solve it?
algebra-precalculus contest-math
algebra-precalculus contest-math
edited 2 hours ago
NoChance
3,79221321
asked 2 hours ago
swagbutton8swagbutton8
61
New contributor
swagbutton8 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 2 hours ago
NoChance
3,79221321
asked 2 hours ago
swagbutton8swagbutton8
61
New contributor
swagbutton8 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 2 hours ago
NoChance
3,79221321
edited 2 hours ago
NoChance
3,79221321
edited 2 hours ago
NoChance
3,79221321
3,79221321
asked 2 hours ago
swagbutton8swagbutton8
61
New contributor
swagbutton8 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 2 hours ago
swagbutton8swagbutton8
61
asked 2 hours ago
swagbutton8swagbutton8
61
61
New contributor
swagbutton8 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
swagbutton8 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
swagbutton8 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
1
$begingroup$
Do you know how to find a derivative?
$endgroup$
– R. Burton
2 hours ago
$begingroup$
Simply $x^2+5x+3=x+b$ must have only one solution, i.e. $x^2+4x+(3-b)=0$ should have zero discriminant.
$endgroup$
– the_fox
2 hours ago
$begingroup$
A Parabola could have many tangent lines...However, it has only 1 min. value, may be this one is the one you are after. More here:desmos.com/calculator/zz7e1nwgf9 and here:info:math.stackexchange.com/questions/92165/…
$endgroup$
– NoChance
1 hour ago
1
$begingroup$
@NoChance Your observation would be relevant if the line’s equation were of the form $y=b$. The line in the problem is not horizontal, though.
$endgroup$
– amd
42 mins ago
$begingroup$
@amd, thanks for your comment. I am not sure which tangent line one should pick then?
$endgroup$
– NoChance
10 mins ago
add a comment |
1
$begingroup$
Do you know how to find a derivative?
$endgroup$
– R. Burton
2 hours ago
$begingroup$
Simply $x^2+5x+3=x+b$ must have only one solution, i.e. $x^2+4x+(3-b)=0$ should have zero discriminant.
$endgroup$
– the_fox
2 hours ago
$begingroup$
A Parabola could have many tangent lines...However, it has only 1 min. value, may be this one is the one you are after. More here:desmos.com/calculator/zz7e1nwgf9 and here:info:math.stackexchange.com/questions/92165/…
$endgroup$
– NoChance
1 hour ago
1
$begingroup$
@NoChance Your observation would be relevant if the line’s equation were of the form $y=b$. The line in the problem is not horizontal, though.
$endgroup$
– amd
42 mins ago
$begingroup$
@amd, thanks for your comment. I am not sure which tangent line one should pick then?
$endgroup$
– NoChance
10 mins ago
1
1
$begingroup$
Do you know how to find a derivative?
$endgroup$
– R. Burton
2 hours ago
$begingroup$
Do you know how to find a derivative?
$endgroup$
– R. Burton
2 hours ago
$begingroup$
Simply $x^2+5x+3=x+b$ must have only one solution, i.e. $x^2+4x+(3-b)=0$ should have zero discriminant.
$endgroup$
– the_fox
2 hours ago
$begingroup$
Simply $x^2+5x+3=x+b$ must have only one solution, i.e. $x^2+4x+(3-b)=0$ should have zero discriminant.
$endgroup$
– the_fox
2 hours ago
$begingroup$
A Parabola could have many tangent lines...However, it has only 1 min. value, may be this one is the one you are after. More here:desmos.com/calculator/zz7e1nwgf9 and here:info:math.stackexchange.com/questions/92165/…
$endgroup$
– NoChance
1 hour ago
$begingroup$
A Parabola could have many tangent lines...However, it has only 1 min. value, may be this one is the one you are after. More here:desmos.com/calculator/zz7e1nwgf9 and here:info:math.stackexchange.com/questions/92165/…
$endgroup$
– NoChance
1 hour ago
1
1
$begingroup$
@NoChance Your observation would be relevant if the line’s equation were of the form $y=b$. The line in the problem is not horizontal, though.
$endgroup$
– amd
42 mins ago
$begingroup$
@NoChance Your observation would be relevant if the line’s equation were of the form $y=b$. The line in the problem is not horizontal, though.
$endgroup$
– amd
42 mins ago
$begingroup$
@amd, thanks for your comment. I am not sure which tangent line one should pick then?
$endgroup$
– NoChance
10 mins ago
$begingroup$
@amd, thanks for your comment. I am not sure which tangent line one should pick then?
$endgroup$
– NoChance
10 mins ago
add a comment |
3 Answers
3
active
oldest
votes
$begingroup$
Hint:
$$x^2+5x+3=x+biff x^2+4x+3-b=0,$$ this quadratic equation should have exactly one solution therefore the discriminant $Delta=?$
answered 2 hours ago
HAMIDINE SOUMAREHAMIDINE SOUMARE
3,1471422
$endgroup$
add a comment |
$begingroup$
Note that you like the line $y=x+b$ to be tangent to the parabola. The slope of this line is $ m=1.$ Thus the derivative of your parabola should be the same as the slope of the tangent line. Find the point of the tangency and find the $b$ value so that the line passes through that point.
answered 1 hour ago
Mohammad Riazi-KermaniMohammad Riazi-Kermani
42.2k42061
$endgroup$
add a comment |
$begingroup$
The tangent to parabola has slope $y' = 2x+5$ which should be slope of line =1 at the point of contact. So point of contact is at x=-2. Substituting in parabola,we get y=-3. Now this point lies on line as well.
answered 1 hour ago
TojrahTojrah
5968
$endgroup$
add a comment |
Your Answer
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
swagbutton8 is a new contributor. Be nice, and check out our Code of Conduct.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3201227%2ffinding-a-tangent-line-to-a-parabola%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Hint:
$$x^2+5x+3=x+biff x^2+4x+3-b=0,$$ this quadratic equation should have exactly one solution therefore the discriminant $Delta=?$
answered 2 hours ago
HAMIDINE SOUMAREHAMIDINE SOUMARE
3,1471422
$endgroup$
add a comment |
$begingroup$
Hint:
$$x^2+5x+3=x+biff x^2+4x+3-b=0,$$ this quadratic equation should have exactly one solution therefore the discriminant $Delta=?$
answered 2 hours ago
HAMIDINE SOUMAREHAMIDINE SOUMARE
3,1471422
$endgroup$
add a comment |
$begingroup$
Hint:
$$x^2+5x+3=x+biff x^2+4x+3-b=0,$$ this quadratic equation should have exactly one solution therefore the discriminant $Delta=?$
answered 2 hours ago
HAMIDINE SOUMAREHAMIDINE SOUMARE
3,1471422
$endgroup$
Hint:
$$x^2+5x+3=x+biff x^2+4x+3-b=0,$$ this quadratic equation should have exactly one solution therefore the discriminant $Delta=?$
answered 2 hours ago
HAMIDINE SOUMAREHAMIDINE SOUMARE
3,1471422
answered 2 hours ago
HAMIDINE SOUMAREHAMIDINE SOUMARE
3,1471422
answered 2 hours ago
HAMIDINE SOUMAREHAMIDINE SOUMARE
3,1471422
answered 2 hours ago
HAMIDINE SOUMAREHAMIDINE SOUMARE
3,1471422
3,1471422
add a comment |
add a comment |
$begingroup$
Note that you like the line $y=x+b$ to be tangent to the parabola. The slope of this line is $ m=1.$ Thus the derivative of your parabola should be the same as the slope of the tangent line. Find the point of the tangency and find the $b$ value so that the line passes through that point.
answered 1 hour ago
Mohammad Riazi-KermaniMohammad Riazi-Kermani
42.2k42061
$endgroup$
add a comment |
$begingroup$
Note that you like the line $y=x+b$ to be tangent to the parabola. The slope of this line is $ m=1.$ Thus the derivative of your parabola should be the same as the slope of the tangent line. Find the point of the tangency and find the $b$ value so that the line passes through that point.
answered 1 hour ago
Mohammad Riazi-KermaniMohammad Riazi-Kermani
42.2k42061
$endgroup$
add a comment |
$begingroup$
Note that you like the line $y=x+b$ to be tangent to the parabola. The slope of this line is $ m=1.$ Thus the derivative of your parabola should be the same as the slope of the tangent line. Find the point of the tangency and find the $b$ value so that the line passes through that point.
answered 1 hour ago
Mohammad Riazi-KermaniMohammad Riazi-Kermani
42.2k42061
$endgroup$
Note that you like the line $y=x+b$ to be tangent to the parabola. The slope of this line is $ m=1.$ Thus the derivative of your parabola should be the same as the slope of the tangent line. Find the point of the tangency and find the $b$ value so that the line passes through that point.
answered 1 hour ago
Mohammad Riazi-KermaniMohammad Riazi-Kermani
42.2k42061
answered 1 hour ago
Mohammad Riazi-KermaniMohammad Riazi-Kermani
42.2k42061
answered 1 hour ago
Mohammad Riazi-KermaniMohammad Riazi-Kermani
42.2k42061
answered 1 hour ago
Mohammad Riazi-KermaniMohammad Riazi-Kermani
42.2k42061
42.2k42061
add a comment |
add a comment |
$begingroup$
The tangent to parabola has slope $y' = 2x+5$ which should be slope of line =1 at the point of contact. So point of contact is at x=-2. Substituting in parabola,we get y=-3. Now this point lies on line as well.
answered 1 hour ago
TojrahTojrah
5968
$endgroup$
add a comment |
$begingroup$
The tangent to parabola has slope $y' = 2x+5$ which should be slope of line =1 at the point of contact. So point of contact is at x=-2. Substituting in parabola,we get y=-3. Now this point lies on line as well.
answered 1 hour ago
TojrahTojrah
5968
$endgroup$
add a comment |
$begingroup$
The tangent to parabola has slope $y' = 2x+5$ which should be slope of line =1 at the point of contact. So point of contact is at x=-2. Substituting in parabola,we get y=-3. Now this point lies on line as well.
answered 1 hour ago
TojrahTojrah
5968
$endgroup$
The tangent to parabola has slope $y' = 2x+5$ which should be slope of line =1 at the point of contact. So point of contact is at x=-2. Substituting in parabola,we get y=-3. Now this point lies on line as well.
answered 1 hour ago
TojrahTojrah
5968
answered 1 hour ago
TojrahTojrah
5968
answered 1 hour ago
TojrahTojrah
5968
answered 1 hour ago
TojrahTojrah
5968
5968
add a comment |
add a comment |
swagbutton8 is a new contributor. Be nice, and check out our Code of Conduct.
swagbutton8 is a new contributor. Be nice, and check out our Code of Conduct.
swagbutton8 is a new contributor. Be nice, and check out our Code of Conduct.
swagbutton8 is a new contributor. Be nice, and check out our Code of Conduct.
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3201227%2ffinding-a-tangent-line-to-a-parabola%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
1
$begingroup$
Do you know how to find a derivative?
$endgroup$
– R. Burton
2 hours ago
$begingroup$
Simply $x^2+5x+3=x+b$ must have only one solution, i.e. $x^2+4x+(3-b)=0$ should have zero discriminant.
$endgroup$
– the_fox
2 hours ago
$begingroup$
A Parabola could have many tangent lines...However, it has only 1 min. value, may be this one is the one you are after. More here:desmos.com/calculator/zz7e1nwgf9 and here:info:math.stackexchange.com/questions/92165/…
$endgroup$
– NoChance
1 hour ago
1
$begingroup$
@NoChance Your observation would be relevant if the line’s equation were of the form $y=b$. The line in the problem is not horizontal, though.
$endgroup$
– amd
42 mins ago
$begingroup$
@amd, thanks for your comment. I am not sure which tangent line one should pick then?
$endgroup$
– NoChance
10 mins ago