Write an equation for a quadratic function in vertex form with Vertex (-1, 6) that passes through the point (-3,4).

Step-by-step explanation:

We want to write the equation for a quadratic function in vertex form with vertex at (-1, 6) that passes through the point (-3, 4).

Vertex form is given by:

Where (h, k) is the vertex and a is the leading coefficient.

Since our vertex is at (-1, 6), h = -1 and k = 6. Substitute:

Simplify:

Next, since the quadratic passes through the point (-3, 4), f(x) = 4 when x = -3. Substitute:

Solve for a. Simplify:

Hence:

Therefore, our function in vertex form is:

the range is 19

step-by-step explanation:

the range is biggest number minus the smallest, so in this case it would be

41 - 22 = 19