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The vertex of a parabola is at (12,-4), and its axis of symmetry is vertical. One of the x-intercepts is at (-15,0). What is the x-coordinate of the other x-intercept?

 May 22, 2022
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The equation for a parabola is y=ax^2+bx+c. We are given two points, and the axis of symmetry (x=12) which will be plenty for us.

 

The axis of symmetry can be found with the equation -b/2a=12. Solving for b, we get -b=24a, so b=-24a. Now we can turn our equation into:

 

y=ax^2-24ax+c. We can plug in the two points to get the two equations

-4=-144a+c

0=585a+c

Solving the system of linear equations, a=4/729 and c=-260/81. Now we can solve for b=-96/729.

 

Finding the other root of the quadratic 4/729x^2-96/729x-260/81=0, we get the other x-intercept to be (39, 0) or 39.

 May 23, 2022

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