Question

What is the equation of the graph

Answer 1

`y = 2x^2 + 1`

Explanation:

The graph you see there is called a parabola. The general equation for the graph is as below

`y = a*x^2 + b`

To find the equation we need to find the constants a and b. The constant b is just how much we're lifting the parabola by. Notice it's lifted by 1 on the y axis.

To find a it's a little more tricky. Let's use the graph to find a value for a by plugging in values we know. We know that b is 1 from the previous step, and we know that when x=1, y=3. Let's use that!

`3 = a * (1)^2 + 1\\2 = a`

Awesome, we've found both values. And we can write the result.

`y = 2x^2 + 1`

I'll include a plotted graph with our equation just so you can verify it is indeed the same.