Question

Help quick please! I need this asap, it’s an assignment due at 11:59! thx!

Answer 1

`y=-1(x-2)^2+1`

Explanation:

The parabola has the vertex (2, 1) and goes through the point (4, -3).

We will use the vertex form, given by:

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

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

Line 1)

So, by substitution:

`\text{Vertex}=(h,k)=(2,1)\Rightarrow y=a(x-2)^2+1`

Lines 2-4)

Since (4, -3) is a point, y = -3 when x = 4:

`-3=a(4-2)^2+1`

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

`-4=4a\Rightarrow a = -1`

Line 5)

By substitution, we acquire our equation*:

`y=-1(x-2)^2+1`