Question

A quadratic equation that has X-intercepts of (-2,0) and (8,0), a stretch of 3, and the vertex is a minimum.

a. Factored form equation:
b. Vertex form equation:
c. Standard form equation:

Answer 1

a. y = 3 × (x + 2)(x - 8)

b. y = 3·(x - 3)² - 75

c) y = 3·x² - 18·x - 48

Explanation:

The x-intercept of the quadratic equation are (-2, 0), (8, 0)

The stretch of the quadratic equation = 3

We have;

a. The factored form y = 3 × (x + 2)(x - 8)

b. From the vertex form, we have;

y = 3 × (x + 2)(x - 8) = 3·x² - 18·x - 48

y = 3·x² - 18·x - 48

The vertex form a(x - h)² + k

Where;

h = -b/(2·a) = 18/6 = 3

h = 3

k = c - b²/(4·a) = -48 - (18²)/12 = -75

The vertex form 3·(x - 3)² - 75

c) The standard form of the quadratic equation, y = a·x² + b·x + c

The standard form of the quadratic equation is y = 3·x² - 18·x - 48.