SOLUTION: Determine the quadratic function f whose graph is given. The vertex is (2, -8) and the y-intercept is -4.

Algebra ->  Graphs -> SOLUTION: Determine the quadratic function f whose graph is given. The vertex is (2, -8) and the y-intercept is -4.       Log On


   

Question 1111306: Determine the quadratic function f whose graph is given.
The vertex is (2, -8) and the y-intercept is -4.
Found 2 solutions by josgarithmetic, stanbon:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
y=a%28x-2%29%5E2-8------takes care of the vertex

y%2B8=a%28x-2%29%5E2
%28y%2B8%29%2F%28x-2%29%5E2=a

a=%28-4%2B8%29%2F%280-2%29%5E2-------the given point helps to evaluate factor, a.
a=4%2F%282%5E2%29
a=1

highlight%28y=%28x-2%29%5E2-8%29

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Determine the quadratic function f whose graph is given.
The vertex is (2, -8) and the y-intercept is -4.
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Form:: y = ax^2 + bx + c
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Note:: f(0) = c and f(0) = -4, so c = -4
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Using (2,-8) you get -8 = a(2^2)+b(2)-4
-4 = 4a + 2b
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Note:: The vertex occurs where x = -b/(2a)
So, -b/2a = 2
Then -b = 4a
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You now have 2 equations in a and b; solve them by substitution::
-4 = -b + 2b
b = -4
Then a = 1
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Equation:: y = x^2 -4x -4
Cheers,
Stan H.
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