Question 662633: Determine the quardratic function f whose graph given, the vertex is (3,-4) and (2,-1)
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Determine the quardratic function f whose graph given, the vertex is (3,-4) and (2,-1)
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Quadratic functions are equations of parabolas of the standard form: y=A(x-h)^2+k, (h,k)=(x,y) coordinates of the vertex, A=multiplier which affects slope or narrowness of the curve.
equation:
y=A(x-h)^2+k
y=A(x-3)^2-4
plug in coordinates of given point (2,-1) to solve for A
-1=A(2-3)^2-4
-1=A(-1)^2-4
A=3
equation: y=3(x-3)^2-4
=3(x^2-6x+9)-4
=3x^2-18x+27-4
f(x)=3x^2-18x+23
see graph below as visual check on the answer:
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