The parent function of a quadratic, f(x) =x^2 reflected across the x-axis. Write an equation of the transformed quadratic function, g(x), in vertex form

  g(x) = -x^2

Step-by-step explanation:

The vertex of the original function is (0, 0). Reflection across the x-axis does not change that, but it does change the sign of the vertical scale factor (a).

In vertex form, a quadratic is ...

  f(x) = a(x -h)^2 +k . . . . . . . . for vertical scale factor "a" and vertex (h, k)

Since the vertex is (0, 0) and the scale factor is -1 (after reflection), the raw vertex form is ...

  g(x) = -1(x -0)^2 +0

Simplifying a bit, we have ...

  g(x) = -x^2

answer: yes, since the line has a steeper rate of change than the exponential the y-values will be greater and they will only intersect one time.