CPM Homework Help : A2C Problem 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.

Hint:

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

More Help 1:

Set the equation equal to $0$ and factor.

Answer 1:

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

More Help 2:

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

Answer 2:

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