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 a minimum

• If a < 0 then vertex is a maximum

Given

y x² - 8x + 14

(a)

To complete the square

add/ subtract ( half the coefficient of the x- term)² to x² - 8x

y = x² + 2(- 4)x + 16 - 16 + 14

y = (x - 4)² - 2 ← in vertex form

(b)

Since the multiplier a = 1 > 0 then vertex is a minimum

(c)

(h , k ) = (4, - 2 ) ← coordinates of vertex