Question 606858: Consider a quadratic function that has a minimum value of -6, and x-intercepts at (-6,0) and (0,0).
A)Determine the equation of the quadratic function. Show or explain your work.
....please help me! I really want to understand how to do this. I'm not sure how and what the answer would be.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Consider a quadratic function that has a minimum value of -6, and x-intercepts at (-6,0) and (0,0)
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Plot the x-intercepts
Since the minimum y-value is -6
the vertex must be at (-3,-6)
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y = a(x-0)(x-(-6))
Solve for "a":
-6 = a(-3)(-3+6)
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-6 = a(-3)(3)
a = 6/9 = 2/3
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y = (2/3)x(x+6)
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y = (2/3)(x^2+6x)
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y = (2/3)x^2 + 4x
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Cheers,
Stan H.
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