Question

Write the equation of the quadratic function in standard form

Answer 1

Answer: y=x^2+6x+8

Explanation:

Answer 2

`y=x^2+6x+8`

Explanation:

To write the quadratic in standard form, begin by writing it in vertex form

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

Where (h,k) is the vertex of the parabola.

Here the vertex is (-3,-1). Substitute and write:

`y=a(x--3)^2+-1\\y=a(x+3)^2-1`

To find a, substitute one point (x,y) from the parabola into the equation and solve for a. Plug in (-2,0) a x-intercept of the parabola.

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

The vertex form of the equation is
`y=(x+3)^2-1`.

To write in standard form, convert vertex form through the distributive property.

`y=(x+3)^2-1\\y=x^2+6x+9-1\\y=x^2+6x+8`