# Using a graph to find the intersection of two curves can be challenging when the point of intersection is not on gridlines or ends up off the graph. T

Using a graph to find the intersection of two curves can be challenging when the point of intersection is not on gridlines or ends up off the graph. Therefore, it helps to know another way to find the intersection without using a graph.

a. Name the algebraic methods you already know to solve linear systems.

b. Use one of the methods you listed in part

(a) to solve for the intersection of $$\displaystyle{y}={x}^{{2}}−{3}{x}−{10}$$ and $$y=−2x+2$$. Carefully record your steps. Be sure to collaborate with your teammates and check your results along the way. Keep your work for this problem in a safe place. You will need it later in this lesson.

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Latisha Oneil

a. At this point, we know three methods: Equal Values Mwthod, Substitution Method, and Elimination Method.
b. Since both equations have y isolated, we can use the Equal Values Method then solve for x: $$\displaystyle{x}^{{2}}-{3}{x}-{10}=-{2}{x}+{2}$$
Write in standart form: $$\displaystyle{a}{x}^{{2}}+{b}{x}+{c}={0}$$
$$\displaystyle{x}^{{2}}-{3}-{12}={0}$$
Factor the left side: $$(x+3)(x-4)=0$$
By Zero Product Property, $$x+3=0$$
$$x=-3$$
$$x-4=0$$
$$x=4$$
Solve for the corresponding y-values. I used the first equation. When x=-3,
$$y=-2(-3)+2$$
$$y=6+2$$
$$y=8$$
When $$x=4$$, $$y=-2(4)+2$$
$$y=-8+2$$
$$y=-6$$
So, the points of intersection are: (-3.8) and (4,-6)