Question

Write an equation in which the quadratic expression 2x^2 - 12x - 32 equals 0. Show the expression in factored form, find the solution and explain what your solutions mean for the equation. Remember to show your work.

Answer 1

See below.

Explanation:

2x^2 - 12x - 32 = 0

Simplify by dividing by 2:

2(x^2 - 6x - 16) = 0

2(x - 8)(x + 2) = 0

2(x- 8) = 0 so x = 8.

x + 2 = 0 so x = -2.

These 2 values of x mean that the graph of the equation pass through the x axis at the points (-2, 0) and (8, 0).

Answer 2

x = -2 , 8

Explanation:

2x² - 12x - 32 = 0

2(x² - 6x - 16) = 0

2(x² - 8x + 2x - 16) = 0

2[x(x - 8) + 2(x - 8)] = 0

2(x - 8)(x + 2) = 0

Solutions:

x = 8, -2

Means x = -2 and x = 8 are the x-intercepts (points where the curve cuts the x-axis)