Question 667974: Show work, determine the quadratic function of f whose vertex is (1,-1) and passes through (3,7).
F(x)=
Type your answer in the form f(x)=ax˛+bx+c
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Show work, determine the quadratic function of f whose vertex is (1,-1) and passes through (3,7).
F(x)=
Type your answer in the form f(x)=ax˛+bx+c
**
Using standard form of equation for a parabola: y=A(x-h)^2+k, (h,k)=(x,y) coordinates of the vertex
plug in given coordinates of vertex (1,-1)
y=A(x-1)^2-1
plug in given coordinates of given point: (3,7), then solve for A
7=A(3-1)^2-1
7=4A-1
4A=8
A=2
Equation of parabola: (quadratic function):
F(x)=2(x-1)^2-1
F(x)=2(x^2-2x+1)-1
F(x)=2x^2-4x+1
see graph below:
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