Question

At what two points do the graphs of y=2x^2-5x-12 and y=1/2x^2-3x+4 intersect? explain your reasoning.

Answer 1

They have the same y, and x.
set them equal

2x^2-5x-12=1/2 x^2-3x+4

combine terms, solve for x (both values), then compute y for each x.

Answer 2

when i combine the like terms i don't know what the next step is

Answer 3

set y = y
2x^2 - 5x - 12 = (1/2)x^2 - 3x + 4
I don't like fractions, so multiply each term by 2
4x^2 - 10x - 24 = x^2 - 6x + 8
3x^2 -4x - 32 = 0
(x - 4)(3x + 8) = 0
x = 4 or x = -8/3

if x = 4, y = 32 - 20 - 12 = 0
if x = -8/3
y = 128/9 +40/3 - 12 = 140/9

I could have subbed into the other equation to obtain the same y values, since we set them equal

two points are(4,0) and (-8/3, 140/9)