CPM Homework Help : CCA2 Problem 12-103

Without graphing, determine where the graphs of $f(x) = 2x^2 - 3x + 1$ and $g(x) = 4x - 2$ intersect.

Step 1:

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

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

Step 2:

Set the equation equal to $0$ .

$2x^2 - 7x+ 3 = 0$

Step 3:

Factor the polynomial.

$(2x - 1)(x - 3) = 0$

Step 4:

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

$x =$ ¹/₂, $3$

Step 5:

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