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
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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:
{{{ graph( 300, 300, -10, 10, -10, 10,2(x-1)^2-1) }}}