Question

Please help,

Write an equation in which the quadratic expression 2x^2 - 2x - 12 equals 0. Show the expression factored form and explain what your solutions mean for the equation.
Show your work.

20 Points!

Answer 1

See below.

Explanation:

2x^2 - 2x - 12 = 0

2 is a factor so we write:

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

2(x - 3)(x + 2) = 0

The solutions are x = -2 and x = 3 which means that the graph of the equation passes through the x-axis at (-2, 0) and (3, 0). The graph is a parabola opening upwards. Also the multiplier of 2 produces a vertical transformation (stretching) of the graph of x^2 - x - 6.