Question

What is the equation of the following graph in vertex form?

Parabolic function going down from the left through the point (0,12)and through the point (2,0) and turning at the point (4,-4) and going up through the point (6,0) and continuing towards infinity
y = (x − 4)2 − 4
y = (x + 4)2 − 4
y = (x + 2)2 + 6
y = (x + 2)2 + 12

Answer 1

f(x) = (x - 4)² - 4

Explanation:

∵ The general form of the Parabolic function is :

f(x) = (x - h) + k ⇒ where point (h , k) is the turning point

∵ The turning point is (4 , -4)

∴ f(x) = (x - 4)² + -4 = (x - 4)² - 4

To check the answer:

Use the point (6 , 0) ⇒ 0 = (6 - 4)² - 4 ⇒ 0 = 4 - 4

∴ f(x) = (x - 4)² - 4