Vertex form is y = a(x - h)^2 + k. If a quadratic function has the vertex form of y = 3(x + 7)^2 - 2

Question

then what is the reflection point for the y-intercept? (Hint: After you calculate the y-intercept, reflect the point in the axis of symmetry.) Remember to type your point in the form (x,y) without any spaces.

Answer 1

The graph of y = 3(x+7)²-2 is a parabola opening upward with lowest point (vertex) at (-7, -2).  

 

The axis of symmetry is the vertical line that goes through the vertex.  So, in this problem the axis of symmetry is the line x = -7.  

 

The y intercept is found by substituting 0 for x in the original equation.  Doing this, we find that the y-intercept is the point

(0, 145).  

 

Reflecting the point (0, 145) through the line x = -7, we get 

(-14, 145).