Question

use the quadratic formula to find any x-intercept(s) on the graph of the function f(x)=
${2x}^{2} + 2x - 1$

Answer 1

Here a=2, b=2 and c=-1. The discriminant, b^2-4ac, is then 4 - 4(2)(-1), or 12. Because this discriminant is positive, the given function has two real roots which are unequal.

Writing out the quadratic formula with the appropriate a, b and c values:

-2 plus or minus √12

x = ---------------------------------

2(2)

-2 plus or minus 2√3

x = -----------------------------------

4

This can be reduced by dividing all 3 terms by 2:

-1 plus or minus √3

x = ----------------------------------- These are the x- intercepts

2 of the given quadratic.