Question

Write an equation of the parabola that has the same shape as the graph of f(x)=3x^2, but with the point (7,-2) as the vertex

Answer 1

Hello!

$\large\boxed{f(x) = 3(x - 7)^{2} - 2}$

Recall that the transformations form of a parabola is:

f(x) = ±a(b(x-h)) + k where:

a = vertical stretch/compression

b = horizontal stretch/compression

h = horizontal shift, x-coordinate of vertex

k = vertical shift, y-coordinate of vertex

In this instance, the parent function is f(x) = 3x^2. There is a vertical stretch of 3.

However, there is a point (7, -2) that needs to be included. Substitute these values into the transformation formula:

h = 7

k = -2

f(x) = 3(x - 7)² - 2 is the equation with (7, -2) as the vertex.