Question

How do you make an equation of it the given points?

Answer 1

Quadratic equations can be expressed in vertex form as follows: y = a(x - h)^2+ k.

In this equation, the vertex is (h,k). This means you can plug in the values as follows: y = a(x + 2)^2 + 1. Notice in the brackets the - becomes + because it's a -2 we're subbing in.

Now we just need to solve for a to find the general form of the equation. We can do this by subbing in the other point we're giving in the question for x and y as follows:

$y = a(x + 2)^2+1 \\ 10 = a(1 + 2)^2+ 1 \\ 9=9a \\ a=1$

Now that we have a value for a, we can write the general equation for this parabola: y = (x + 2)^2 + 1. (Since a=1 it doesn't need to be explicitly written in the equation).