### Home > INT3 > Chapter 6 > Lesson 6.1.1 > Problem 6-10

6-10.

Algebraically determine where the graphs of *f*(*x*) = 2*x*^{2} – 3*x* + 1 and *g*(*x*) = 4*x* – 2 intersect. Homework Help ✎

Use the Equal Values Method since we want to determine where *f*(*x*) = *x*(*x*).

2*x*^{2} − 3*x* + 1 = 4*x* − 2

Set the equation equal to 0.

2*x*^{2} − 7*x* + 3 = 0

Factor the polynomial.

(2*x* − 1)(*x* − 3) = 0

Use the Zero Product Property to solve for *x*.

*x* = ½, 3

Substitute the *x*-values back into one of the original functions to find their corresponding *y*-values.