Question

Help me please!!!!!!11!

Answer 1

`y=x^2-4x-2`

Explanation:

Standard Form of Quadratic:

`y=ax^2+bx+c`

Vertex Form of Quadratic:

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

h = vertex x

k = vertex y

Think of h and k as the ordered pair (h,k).

Match this ordered pair to the vertex ordered pair.

(h,k) = (2, -6)

Plug in (h,k) into vertex form:

`y = a(x-2)^2-6`

Use other point to solve for a.

`3 = a(5-2)^2-6`

`3=a(3)^2-6`

`3=9a-6`

`9=9a`

`a=1`

Plug a back into vertex form and expand the expression into standard form:

`y=(x-2)^2-6`

`y=(x-2)(x-2)-6`

Use F.O.I.L. method to expand (x-2)(x-2).

F(first):
`x*x=x^2`

O(outer):
`x*-2=-2x`

I(inner):
`-2*x =-2x`

L(last):
`-2*-2=4`

`y=x^2-2x-2x+4-6`

Combine like terms:

`y=x^2-4x-2`