Question

What is the equation of the graph?

Answer 1

`y=2x^2+1`

Explanation:

The general equation for a parabola in vertex form is the following:

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

Where (
`h,k`) is the parabola's vertex and (a) is the stretch and compression factor. As one can see in the given graph, the parabola has a vertex at (0, 1), moreover, it passes through the point (1, 3). Substitute these points into the equation for the parabole, and simplify,

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

Vertex: (0, 1)

`y=a(x-0)^2+1`

A point on the parabola: (1, 3)

`3=a(1-0)^2+1`

`3=a1+1\\3 = a + 1\\`

Inverse operations,

`3=a+1`

`2 = a`

Substitute back into the original expression:

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

`y=2(x-0)^2+1`

Simplify to put in standard form:

`y=2(x-0)^2+1`

`y=2(x)^2+1`

`y=2x^2+1`