SOLUTION: 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.

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)
=============================
y = a(x-0)(x-(-6))
Solve for "a":
-6 = a(-3)(-3+6)
----
-6 = a(-3)(3)
a = 6/9 = 2/3
----
y = (2/3)x(x+6)
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y = (2/3)(x^2+6x)
-
y = (2/3)x^2 + 4x
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Cheers,
Stan H.
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