Question

What is the equation, in vertex form, of the quadratic function that has a vertex at V(−2, −6) and passes through point P(−4, −7)?

Answer 1

f(x) = -¹/₄(x + 2)² - 6

Explanation:

The vertex form of an equation of the parabola:

f(x) = a(x - h)² + k

vertex is (-2, -6) so h = -2, k = -6

so:

f(x) = a(x - (-2))² + (-6)

f(x) = a(x + 2)² - 6

the parabola goes through the point (-4, -7) so for x=-4, f(x)=-7

-7 = a(-4+2)² - 6

-7 +6 = a(-2)² - 6 +6

- 1 = a(4)

a = -¹/₄

Therefore the equation of the parabola in vertex form:

f(x) = -¹/₄(x + 2)² - 6