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sqdancefan

Answer:

  • A(-9/2, 0)
  • B(1, 0)
  • C(0, -9)

Step-by-step explanation:

Given the quadratic equation y = 2x² +7x -9, you want the coordinates of the x- and y-intercepts.

X-intercepts

The values of x where y=0 can be found by factoring the equation.

  y = (2x +9)(2x -2)/2 = (2x +9)(x -1)

The constants 9 and -2 in the binomial terms are factors of the product of leading and trailing coefficients (2)(-9) = -18. Those factors are chosen because their sum is 7, the middle coefficient.

The x-intercepts are the values of x that make these factors zero:

  2x +9 = 0   ⇒   x = -9/2

  x -1 = 0   ⇒   x = 1

Points A and B are ...

  • A(-9/2, 0)
  • B(1, 0)

Y-intercept

The y-value at point C is where x=0. It is the constant in the quadratic equation.

  y = 2(0²) +7(0) -9 = -9

Point C is ...

  • C(0, -9)
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