Question

Use the quadratic function f(x) = 2x^2 + 4x - 15. Find any x intercepts.

Answer 1

So for this function we will be using the quadratic formula, which is $x=\frac{-b+\sqrt{b^2-4ac}}{2a},\frac{-b-\sqrt{b^2-4ac}}{2a}$ , to solve. a = x^2 coefficient, b = x coefficient, and c = constant. Using our equation, we can solve for the zeros (x-intercepts) as such:

$x=\frac{-4+\sqrt{4^2-4*2*(-15)}}{2*2},\frac{-4-\sqrt{4^2-4*2*(-15)}}{2*2}\\ \\ x=\frac{-4+\sqrt{16-(-120)}}{4},\frac{-4-\sqrt{16-(-120)}}{4}\\ \\ x=\frac{-4+\sqrt{136}}{4},\frac{-4-\sqrt{136}}{4}\\ \\ x=1.92,-3.92$

In short, your x-intercepts (rounded to the hundredths) are (1.92,0) and (-3.92,0).