SOLUTION: Suppose a parabola has an axis of symmetry at x=-2, a minimum height at -6, and passes through the point (0,10). What's the equation of the parabola in vertex form?

Question 1062731: Suppose a parabola has an axis of symmetry at x=-2, a minimum height at -6, and passes through the point (0,10). What's the equation of the parabola in vertex form?

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
The axis of symmetry means the vertex x value is at -2
The minimum height is -6, meaning it is convex down or is U shaped. Vertex is at (-2,-6)
That makes the x^2 term positive
The y-intercept is 10.
Vertex form is f(x)= a(x-h)^2+k, where h and k are the vertex coordinates
f(x)=a(x+2)^2-6
when x=0, y=10
substitute
10=a(2^2)-6=4a-6
4a=16
a=4
f(x)=4(x+2)^2-6, 4x^2+16x+10. The first is vertex form.

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