Find an equation of the parabola that satisfies the given conditions. vertex V(−3, 5), axis parallel to the x-axis, and passing through the point (5, 9)

Question

Find an equation of the parabola that satisfies the given conditions.

vertex V(−3, 5), axis parallel to the x-axis, and passing through the point (5, 9)

Answer 1

When you say axis parallel to the x axis, I believe that means axis of symmetry. That means the equation take on this standard form:

(y-k)²=a(x-h)

Next, plug in the vertex (h,k)

(y-5)²=a(x+3)

Then, plug in the point that is given

(9-5)²=a(5+3) Simplify and solve for a

4²=8a

16=8a

a=2

Plug in a to get the final equation.

(y-5)²=2(x+3)