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Question 165604: Write the equation of a parabola that:
A. has x=3 as its axis of symmetry and passes through the points (2,5) & (-1,-25).
B. passes through the points (-3,2), (-2,8), and (1,2).
PLEASE show any graphical or algebraic support needed to provide the solution!!!
Answer by scott8148(6628)   (Show Source):
You can put this solution on YOUR website! the vertex form of the parabola equation is y=a(x-h)^2+k, where (h,k) is the vertex
__ the axis of symmetry goes through the vertex
A. substituting __ 5=a(2-3)^2+k __ 5=a+k
__ substituting __ -25=a(-1-3)^2+k __ -25=16a+k
subtracting the equations __ -25-5=16a+k-a-k __ -30=15a __ -2=a
substituting __ 5=(-2)+k __ 7=k
y=-2(x-3)^2+7
B.the points (-3,2) and (1,2) have the same y value, so the axis of symmetry is midway between them __ x=-1
substituting __ 2=a(-3+1)^2+k __ 2=4a+k
substituting __ 8=a(-2+1)^2+k __ 8=a+k
subtracting the equations __ 2-8=4a+k-a-k __ -6=3a __ -2=a
substituting __ 8=(-2)+k __ 10=k
y=-2(x+1)^2+10
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