a parabola passes through the point (3,5) on its way to the vertex at (7,11). Determine the equation in vertex form that represents this parabola.

Question

A parabola passes through the point (3,5) on its way to the vertex at (7,11). Determine the equation in vertex form that represents this parabola.

Answer 1

Vertex form is y = a(x-h)² + k. h and k are the x and y coordinates of the vertex, respectively. Since we know the vertex, we can simply substitute its coordinates for those values to get y = a(x-7)² + 11. x and y are the coordinates of any point on the parabola, so they should be variables in the final answer. Therefore, all that is left is to find a. Since we know another point on the parabola, we can substitue its coordinates into the equation: 5 = a(3-7)² + 11. Now you can just do some regular old algebra to solve for a.