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 = 3x2 - 6x + 11 become after completing the square?

Answer 1

i end up getting k=56

Answer 2

its not one of my answers

Answer 3

\[y=3(x^2-2x)+11\] what is half of \(-2\) ?

Answer 4

oh

Answer 5

-1

Answer 6

\[y=3(x-1)^2+k\] find \(k\) as before, put \(x=-1\) in \(y=3x^2-6x+11\)

Answer 7

oops hold on i think i made a mistake here

Answer 8

don't replace \(x\) by \(-1\)
replace \(x\) by \(1\)

Answer 9

why?

Answer 10

\[y=3(x-1)^2+k\] the vertex is \((1,k)\)

Answer 11

if you put \(x=1\) you get
\[y=3(1-1)+k=k\]

Answer 12

so put \(1\) in the original equation to find \(k\)

Answer 13

8

Answer 14

yes
so
\[y=3(x-1)^2+8\]