Question

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?

Answer 1

9

Explanation:

The parabola is symmetric about its axis of symmetry, which passes through the vertex. Since one of the x-intercepts is three units to the right of 12, the other x-intercept must be three units to the left of 12. Thus, its x-coordinate is 9.

Answer 2

9

Explanation:

Since the axis of symmetry is vertical and the vertex of the parabola is at (12,-4), the vertical line x=12 is the axis of symmertry. The x-distance between the axis of symmetry and the first x intercept (15,0) is equal to 15-12=3. Hence, this x-intercept is 3 units to the right of the axis, and because it is symmetric, the other x-intercept must be 3 units to the left of the axis, so its x-coordinate must be 12-3=9. Then, the other x-intercept is at the point (9,0)