CPM Homework Help : AC Problem 12-50

Find the point(s) of intersection of the line and parabola below. Be sure to check each point by substituting it back into both equations.

$\begin{array}{l} y = 3x^2 - 5x + 2 \\ y = 4x + 2 \end{array}$

Step 1:

Set the equations equal to each other.

$4x+2=3x^2-5x+2$

Step 2:

Set the equation equal to zero.

$0=3x^2-9x$

Step 3:

Factor and Solve.

$\left. \begin{array} { l } { 0 = 3 x ( x - 3 ) } \\ { x = 0 \text { and } 3 } \end{array} \right.$

Step 4:

Check these answers by substituting them back into the original equations.

Answer:

Points of intersection are $\left(3,14\right)$ and $\left(0,2\right)$ .