what function is equivalent to f(x)=(1)/(4)(x-2)^(2)+3

Answer 1

Hi Aliyah!

Quadratic functions have two forms (Vertex Form and Standard Form). Your goal is to transform your function from vertex to standard form.

Vertex Form: f(x)=1/4(x-2)²+3

First, expand (x-2)²

(x-2)² =(x-2)(x-2)

=x(x-2)-2(x-2)

=x²-2x-2x+4

=x²-4x+4

Then, substitute expanded expression back into function

f(x)=1/4(x²-4x+4)+3

Finally, distribute and simplify by combining like terms.

How to check your work: Graph f(x)=1/4(x-2)²+3 and your final answer. If they are equivalent functions they will have identical graphs.