Question

What is the equation of the graph?

Answer 1

Answer:

$y=2x^2+1$

Step-by-step 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:

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

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

$y=2x^2+1$