# Determine when y = x^2 + bx + 17 has horizontal tangent

• gillgill
In summary, the student is trying to find a value for the constant b in order to have a horizontal tangent at (2,21+2b). They are also trying to learn more about how to plot curves and why a certain point was chosen.
gillgill
am i doing this right?
Determine a value of the constant b so that the graph of y=x^2+bx+17 has a horizontal tangent at (2, 21+2b)
ans: y'(2)=0
y'=2x+b
0=2(2)+b
b=-4
what do u need the y-coordinate (21+2b)for?
My teacher also requires me to draw a diagram...can anybody show me a diagram of this problem?

Did you try plotting your original equation with the value you calculated for b?
From that plot you will see why you need to use the point(2,21+2b).
(Hint: it has to do with the graphical interpretation for taking the first derivative of your equation)

If you are having a problem drawing the diagram.. Try calculating some ordered pairs using a range of x values (say from -10 to 10) and plug that into your original equation. You already have b, so you should be able to calculate all your y-values. Then plot these ordered pairs on some graph paper.

Last edited:
my friend taught me that
21+2(-4)=13
(2)^2+(-4)(2)+17=13
i am not too sure why he did that...

gillgill said:
my friend taught me that
21+2(-4)=13
(2)^2+(-4)(2)+17=13
i am not too sure why he did that...
What does that suggest to you about the point(2,13) and the two
equations you are now working with?

After you plot the ordered pairs as i suggested, from your initial equation y(x)
Do the same thing for the second equation y'(x) and note what is happening.

gillgill said:
am i doing this right?
...
You could have also done it by finding the correct vertex of the parabola.
gillgill said:
...
what do u need the y-coordinate (21+2b)for?
Nothing.
=gillgill said:
My teacher also requires me to draw a diagram...can anybody show me a diagram of this problem?
It's a standard parabola translated a little. Complete the square to find the x and y offsets.

How did you make out plotting your curves?
Did you see why need to use the point(2,21+2b)?

## 1. What is a horizontal tangent?

A horizontal tangent is a line that is parallel to the x-axis and touches a curve at only one point. This point is known as the point of tangency.

## 2. How do you determine when a curve has a horizontal tangent?

A curve has a horizontal tangent when its derivative is equal to 0. In other words, the slope of the tangent line at that point is 0.

## 3. What is the equation for finding the horizontal tangent for y = x^2 + bx + 17?

To find the horizontal tangent for y = x^2 + bx + 17, you need to take the derivative of the function and set it equal to 0. The resulting equation will give you the x-value(s) of the point(s) where the curve has a horizontal tangent.

## 4. How do you solve for the x-value(s) of the horizontal tangent for y = x^2 + bx + 17?

To solve for the x-value(s) of the horizontal tangent, you will need to use the quadratic formula. The resulting solutions will give you the x-value(s) of the point(s) where the curve has a horizontal tangent.

## 5. Can a curve have more than one horizontal tangent?

Yes, it is possible for a curve to have more than one horizontal tangent. This occurs when the curve intersects the x-axis at multiple points where the derivative is equal to 0.

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