Question

Write the equation for the quadratic function in standard form

Answer 1

`y=x^2+6x+7`

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,-2). Substitute and write:

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

To find a, substitute one point (x,y) from the parabola into the equation and solve for a. Plug in (0,7) a y-intercept of the parabola.

`7=a((0)+3)^2-2\\7=a(3)^2-2\\7=9a-2\\9=9a\\1=a`

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

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

`y=(x+3)^2-2\\y=(x^2+6x+9)-2\\y=x^2+6x+7`