### Home > A2C > Chapter 13 > Lesson 13.2.1 > Problem13-106

13-106.

Without graphing, determine where the graphs of $f\left(x\right) = 2x^{2} − 3x + 1$ and $g\left(x\right) = 4x − 2$ intersect.

Substitute $4x − 2$ for y in the first equation.
$y = 2x^{2} − 3x + 1$
$y = 4x − 2$

Set the equation equal to $0$ and factor.

$x=\frac{1}{2}\text{ and }x=3$

Substitute each value of $x$ into the second equation and solve for $y$.

$\text{They intersect at }\left(\frac{1}{2}, 0\right)\text{ and }(3, 10)$