Question 671567: Find an equation in standard form of the parabola (1,-2), (2,-2), (3,-4)
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Find an equation in standard form of the parabola (1,-2), (2,-2), (3,-4)
Quadratic equation:
y=Ax^2+Bx+C
..
-2=A+B+C
-2=4A+2B+C
-4=9A+3B+C
..
0=-3A-B
2=-5A-B
subtract
-2=2A
A=-1
B=-3A=3
C=-2-A-B=-2+1-3=-4
..
Quadratic Equation: y=-x^2+3x-4
Standard form of equation for a parabola: y=A(x-h)^2+k, (h,k)=(x,y) coordinates of the vertex
complete the square
y=-(x^2-3x+9/4)+4+9/4
y=-(x-3/2)^2-7/4 (equation of parabola)
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