Question

The parabola y = a ² + k has vertex (0, -14) and passesthrough the point (5,6). Find its equation.NOTE: Enter the exact answer.y =

Answer 1

The general expression for the parabola is

`y=a(x-h)^2+k`

Where h and k represent the coordinates of its vertex.

h is the x-coordinate

k is the y-coordinate

If the vertex is (0,-14), then h=0 and k=-14, so the formula for the paravola will be:

`y=a(x-0)^2-14`

Now using the coordinates of the point (5,6) to replace in the formula, you can clear the value of "a"

y= 6

x= 5

`\begin{gathered} y=a(x-0)^2-14 \\ y=ax^2-14 \\ 6=a(5)^2-14 \\ 25a=20 \\ a=0.80 \end{gathered}`

a=0.80

The formula for the parabola is

`y=0.8(x-0)^2-14`