Question

If f(x) = x^2 is vertically stretched by a factor of 3 and shifted down 7 to form g(x), which of the following equations best represents the new graph?

Answer 1

g(x) = 3x² - 7

Explanation:

Transformations of Parent Graph: f(x) = a(bx - h)² + k

a is vertical shrink or stretch

b is horizontal shrink or stretch

(h, k) is the vertex

k is vertical movement

We are given that a = 3, k = -7, so simply plug it into the formula:

g(x) = 3(x - 0)² - 7

g(x) = 3x² - 7

Answer 2

g(x) = 3x^2-7

Explanation:

f(x) = x^2 is vertically stretched by a factor of 3 and shifted down 7 to form g(x)

we have

g(x) = 3x^2-7

3 = vertical stretch factor

-7 = translation downwards 7 units.