Question

What does the quadratic function f(x)=x^2-10x+9 look like when it is rewritten in the form f(x) = a (x-h) + k

Answer 1

When
`f(x)=x^2-10x+9` is written in the form
`f(x)=a(x-h)^2+k`, it looks like
`f(x)=(x-5)^2-16`

Step-by-step explanation

To write
`f(x)=x^2-10x+9` in the form
`f(x)=a(x-h)^2+k`, we have to complete the squares.

We add and subtract half the coefficient of
`x` square.

`f(x)=x^2-10x+(-5)^2-(-5)^2+9`

The first three terms of the function is now a perfect square.

`f(x)=(x-5)^2-25+9`

We now simplify rto obtain,

`\Rightarrow f(x)=(x-5)^2-16`