### Home > INT3 > Chapter 6 > Lesson 6.1.1 > Problem6-10

6-10.

Algebraically determine where the graphs of $f(x) = 2x^2 - 3x + 1$ and $g(x) = 4x - 2$ intersect.

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

$2x^2 − 3x + 1 = 4x − 2$

Set the equation equal to $0$.

$2x^2 − 7x + 3 = 0$

Factor the polynomial.

$(2x − 1)(x − 3) = 0$

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

$x=\frac{1}{2},3$

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