Question

Write an equation in standard form of the parabola that has the same shape as the graph of f(x)=7x^2, but with (4,3) as the vertex.
g(x) = __________

Answer 1

Answer:

g(x) = 7x² − 56x + 115

Step-by-step explanation:

f(x) = 7x²

This parabola has a vertex of (0, 0).

To shift f(x):

f(x) − k = 7(x − h)²

where h is the horizontal shift and k is the vertical shift.

We want the new vertex to be (4, 3), so we want to shift f(x) 4 units to the right and 3 units up.

g(x) − 3 = 7(x − 4)²

This is in vertex form.  We want to write it in standard form.  So simplify:

g(x) − 3 = 7(x² − 8x + 16)

g(x) − 3 = 7x² − 56x + 112

g(x) = 7x² − 56x + 115