Question 479050
_Find f(x)=ax^2+bx+c, given that f(0)=-8 and the vertex is (1,-9)
_Find f(x)=ax^2+bx+c, given that the vertex is (2,-1) and the point (4,3) lies on the parabola
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First equation:
Standard form of a parabola: y=A(x-h)^2+k, with (h,k) being the (x,y) coordinates of the vertex.
using given point (0,-8) and vertex (1,-9) to solve for A:
-8=A(0-1)^2-9
1=A
Equation:
y=(x-1)^2-9
f(x)=x^2-2x+1-9
Equation:
f(x)=x^2-2x-8
..
Second Equation:
using given point (4,3) and vertex (2,-1) to solve for A:
3=A(4-2)^2-1
4=4A
A=1
Equation:
y=(x-2)^2-1
f(x)=x^2-4x+4-1
Equation:
f(x)=x^2-4x+3