Question

Please help me! ASAP!!!!!!

Answer 1

D

Explanation:

y = a
`x^(2)` + bx + c is an equation for a parabola in standard form.

y = a(x - h)² + k is the equation for a parabola in vertex form.

We use y = because the parabola opens vertically.

The vertex is the point on the curve of the parabola, so either the lowest or highest point depending on whether it opens up or down.

We are given the vertex of (1,3), is the vertex formula h is the x and k is the y.

(h,k) or in this case (1,3).

Let's substitute the vertex.

y = a(x - 1)² + 3

To find a, we use the other point (2,6) to substitute in x and y to solve.

x = 2 y = 6

6 = a(2 - 1)² + 3

6 = a(1)² + 3

6 = a(1) + 3

6 = a + 3 Subtract 3 from each side.

6 - 3 = a + 3 - 3

6 - 3 = a

3 = a

Now we have all the elements of the equation.

a = 3

h = 1

k = 3

y = 3(x - 1)² + 3

So the answer is D.