Algebra
posted by Frank .
At what two points do the graphs of y=2x^25x12 and y=1/2x^23x+4 intersect? explain your reasoning.

They have the same y, and x.
set them equal
2x^25x12=1/2 x^23x+4
combine terms, solve for x (both values), then compute y for each x. 
when i combine the like terms i don't know what the next step is

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)
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