Finding the Reflection Point Of y = 3(x + 7)^2 - 2

Question

Vertex form is y = a(x - h)^2 + k. If a quadratic function has the vertex form of y = 3(x + 7)^2 - 2, then what is the reflection point for the y-intercept?

 

Thank you! 

Answer 1

To find the reflection point of the y-intercept, we focus on the x-coordinates.  The distance between the vertex's x-coordinate and the x-coordinate of the y-intercept is the same distance between the vertex's x-coordinate and the desired point's x-coordinate.  This is because the vertex acts as an axis of symmetry.

 

The vertex of the parabola is (-7, -2).   The y-intercept is (0, 145).

 

The distance between the two x-coordinates is 7.  Therefore, the x-coordinate of the reflection point is -14.

 

 

Evaluate y when x=-14 to find the reflection point.