How do you solve y = 3x + 12 and y = x^2 + 2x - 18?

1 Answer
David B.
May 2, 2016

The points of intersections are: (6,30) and (-5,-3)

Explanation:

We are looking for the intersection of a line and a parabola. In other words, we want the points where if we put the same x into both equations, we get the same y, therefore we should set the two y's equal to each other to get the equation:

3x+12 = x^2+2x-18

which we can simplify to

0=x^2-x-30

Now we can use the quadratic equation to find the roots of our new quadratic where a=1, b=-1, and c=-30

x=(1+-sqrt(1+120))/2 implies 6,-5

To find the corresponding y values we can use either equation, but it's simpler to use the line:

y=3x+12 implies 30,-3

So the points of intersections are: (6,30) and (-5,-3)

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