Algebra

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

  • Algebra -

    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.

  • Algebra -

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

  • Algebra -

    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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