Question

Complete the square to write each equation in vertex form. Then, state whether the vertex is a minimum or a maximum and give its coordinates.

Answer 1

see explanation

Explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

• If a > 0 then vertex is minimum

• If a < 0 then vertex is maximum

Given

y = x² + 4x + 2

(a)

To complete the square

add/ subtract ( half the coefficient of the x- term)² to x² + 4x

y = x² + 2(2)x + 4 - 4 + 2

y = (x + 2)² - 2

(b)

Since a = 1 > 0 then vertex is minimum

(c)

(h, k ) = (- 2, - 2 ) ← coordinates of vertex

Answer 2

a) y(x) = (x + 2)^2 -2

b) minimum

c) (-2, -2)