SOLUTION: A parabola passes through (-2,0),(4,0) and (5,14). Find the equation of the axis of symmetry. Find the equation of the line perpendicular to the Y-axis that passes through exactl

Question 139966: A parabola passes through (-2,0),(4,0) and (5,14).
Find the equation of the axis of symmetry.
Find the equation of the line perpendicular to the Y-axis that passes through exactly one point of the parabola.
find the equation of the parabola.
I just do not know where to start, what to look for first. Please help. Thankyou.
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
the first two points have the same y-coordinate, so the axis of symmetry is a vertical line (x=?) midway between them
__ x=(-2+4)/2 __ x=1

the y value of the first two points is zero, so these are the roots of the quadratic equation
__ if -2 and 4 are roots, then x+2 and x-4 are factors
__ there may also be a constant factor that is related to the shape of the graph

y=k(x+2)(x-4) __ using the 3rd point __ 14=k(5+2)(5-4) __ 2=k
__ so y=2(x+2)(x-4)

the line through one point passes through the vertex, which lies on the axis of symmetry
__ substituting __ y=2(1+2)(1-4) __ y=-18
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