### Home > CCA2 > Chapter Ch12 > Lesson 12.2.1 > Problem12-103

12-103.

Without graphing, 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 $f(x) = g(x)$.

$2x^2 - 3x + 1 = 4x - 2$

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 $x$.

$x =$ 1/2, $3$

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