SOLUTION: x −2 −1 0 1 2 y 9 4 1 0 1 Use the table of values that represent points on the graph of a quadratic function. By determining the vertex and axis of sy

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Question 1153438: x −2 −1 0 1 2
y 9 4 1 0 1
Use the table of values that represent points on the graph of a quadratic function. By determining the vertex and axis of symmetry, find the general form of the equation of the quadratic function.
y =

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

x| -2,+-1, 0, 1,+2
y|+9, 4, 1,+0, 1
y=ax%5E2%2Bbx%2Bc..........use given x and y values to calculate coefficients a, b, and constant c

9=a%28-2%29%5E2%2Bb%28-2%29%2Bc
9=4a-2b%2Bc............eq.1

4=a%28-1%29%5E2%2Bb%28-1%29%2Bc
4=a-b%2Bc............eq.2
1=a%280%29%5E2%2Bb%280%29%2Bc
1=c............eq.3

go to
9=4a-2b%2Bc............eq.1, plug in c
9=4a-2b%2B1............solve for b
2b=4a-9%2B1
2b=4a-8
b=2a-4..........1a
go to
4=a-b%2Bc............eq.2, plug in c
4=a-b%2B1...........solve for b
b=a-4%2B1
b=a-3..........2a

from 1a and 2a we have
2a-4=a-3.......solve for+a
2a-a=4-3
a=1
go to
b=a-3..........2a,plug in a
b=1-3
b=-2

your equation is:
y=x%5E2-2x%2B1

determining the vertex: write it in vertex form
y=%28x-1%29%5E2%2B0=> the vertex is at (1,0)
and axis of symmetry is x=1
the general form of the equation of the quadratic function:
ax%5E2+%2B+bx+%2B+c+=+0=> in your case x%5E2+-2x+%2B+1=+0