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?

Question

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Answer 1

The vertex of y = a(x-h)²+k is (h,k).

 

So, for the given function, the vertex is (-7,-2).

 

The graph of the given function is a parabola with axis of symmetry the vertical line that goes through the vertex.

 

So, the axis of symmetry is the line x = -7.

 

The y-intercept is found by plugging in 0 for x.  Doing this, the y-intercept is (0, 145).

 

The y-intercept is 7 units to the right of the axis of symmetry.  So, if we reflect across the axis of symmetry, the y-intercept is reflected 7 units to the left of the axis of symmetry and has the same y-coordinate as the unreflected point.  Thus, the y-intercept is reflected to the point (-14,145).  

 

 

 

 

Answer 2

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.