Mathematics
Emma99
2016-04-12 23:12:27
The vertex of a parabola is (-1.5, -12.5), and its y-intercept is (0, -8). The x-intercepts of the parabola are
ANSWERS
BernitaRafala
2016-04-13 05:00:53

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.

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