SOLUTION: I have been working on this math problem and I can't figure it out. I was wondering if someone could help me? Please and Thank You!! I would deeply appreciate it!! Writing Quadr

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Question 183832This question is from textbook Algebra and Trigonometry Structure and Method book 2
: I have been working on this math problem and I can't figure it out. I was wondering if someone could help me? Please and Thank You!! I would deeply appreciate it!!
Writing Quadratic Equations and Functions
Find a quadratic function F(x)=ax^2+bx+c for each parabola described.
maximum value 6 when x=-2; one zero is 1 This question is from textbook Algebra and Trigonometry Structure and Method book 2

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Find a quadratic function F(x)=ax^2+bx+c for each parabola described.
maximum value 6 when x=-2; one zero is 1
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Maximum occurs when x = -b/2a
So, you have -b/2a = -2
b = 4a
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Substitute and you have
f(x) = ax^2 +(4a)x + c
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Then f(-2) = 4a -8a + c = 6
c = 4a + 6
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Substitute to get:
f(x) ax^2 +(4a)x + 4a + 6
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Then f(1) = a + 4a + 4a + 6 = 1
9a + 6 = 1
9a = -5
a = -5/9
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b = 4a = -20/9
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c = 4a+6 = -20/9 + 54/9 = 34/9
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Equation:
y = (-5/9)x^2 -(20/9)x + (34/9)
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Cheers,
Stan H.
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