The general equation of a parabola is y=ax^2+bx+c At the y-intercept, x=0 and y= -8: -8 = a(0)^2 + b(0) + c. Thus, c = -8. So, our equation becomes y = ax^2 + bx - 8. Next, substitute -1.5 for x and -12.5 for y. Then, -12.5 = a(-1.5)^2 + b(-1.5) - 8. This simplifies to -4.5 = a(2.25) - 1.5b. Next, take advantage of the info that the vertex is at x= -1.5. The formula for the vertex is x=-b/(2a). Letting this formula = -1.5, -1.5 = -b/(2a). We can then solve for b: 1.5 = b/(2a), or 3a = b. Now go back to the equation we derived previously: -4.5 = a(2.25) - 1.5b. Substitute 3a for b: -4.5 = a(2.25) - 1.5(3a). Then -4.5 = -2.25a, and a = 4.5/2.25 = 2. Last, substitute a = 2 into 3a=b to determine the value of b. b=3(2) = 6. Therefore, your equation is y=2x^2 + 6x - 8. Check this result. Substitute the coordinates of the vertex (-1.5,-12.5) into this equation. Is the equation still true? If so, your equation correctly represents this parabola.

The vertex of a parabola is (-1.5, -12.5), and its y-intercept is (0, -8).
The x-intercepts of the parabola are

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2016-04-13 05:00:53

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