Put the function into factored form with integer coefficient

Put the function into factored form with integer coefficients and then identify any horizontal intercepts. y = 2x^2 + 5x - 12 Evaluate the discriminant of f(x) = 2x^2 + 3x - 1. Use the discriminant to determine the nature of the zeros of the function, and how many (if any) horizontal intercepts. Find the solutions, real or complex, of the function, f(x) - x^2 - 6x + 18.

Solution

1) y = 2x^2 + 5x -12 = (x + 4)(2x - 3)

Horizontal intercepts ======> y = 0 ====> (-4, 0), (3/2, 0)

2) f(x) = 2x^2 + 3x - 1

a = 2, b = 3, c = -1

Discriminant = b^2 - 4ac = 9 - 4*2*(-1) = 17

Horizontal intercepts = [(-3 + sqrt(17))/4, 0],   [(-3 - sqrt(17))/4, 0]

3) f(x) = x^2 - 6x + 18

x = [-b + (b^2 - 4ac)]/2a = 3 + 3i

and x = [-b - (b^2 - 4ac)]/2a = 3 - 3i