Question

A quadratic function is much easier to graph when written in the following form.

y = a(x - h)2 + k

To convert an equation from the form y = ax2 + bx + c into the form y = a(x - h)2 + k use completing the square.

What does the equation y = x2 - 10x + 5 become after completing the square?

Answer 1

how do i do this?

Answer 2

\[y = x^2 - 10x + 5 \] you want to write it as
\[y=a(x-h)^2+k\] right?

Answer 3

yes

Answer 4

it should be clear that \(a=1\) because you are starting with \(x^2\) and not for example \(2x^2\) in which case you would have \(a=2\) so it must look like
\[y=(x-h)^2+k\]

Answer 5

then it is easy
what is half of \(-10\) ?

Answer 6

-5?

Answer 7

lol yes
so it is '
\[y=(x-5)^2+k\]

Answer 8

to find \(k\) put \(5\) for \(x\) in
\[y=x^2-10x+5\] i.e. compute
\[5^2-10\times 5+5\] and that will give you \(k\)

Answer 9

let me know when you get \(k=-20\)

Answer 10

i got -20 already

Answer 11

k
then you are done
it is
\[y=(x-5)^2-20\]

Answer 12

ty so much!!!