Question

Using the completing-the-square method, rewrite f(x) = x2 + 4x − 1 in vertex form

Answer 1

Group the terms like this
\[f(x)=(x^2+4x)-1\]
Take the coefficient of x, divide it by 2 and square it.
What's \(\left( \frac{ 4 }{ 2 } \right)^2\) ?

Answer 2

4

Answer 3

Right, so add 4 inside the parentheses.
This means you also have to subtract 4 outside, so the equation doesn't change.
\[f(x)=(x^2+4x+4)-1-4\]

Answer 4

Now factor the part in parentheses, and combine like terms on the outside

Answer 5

so would it be f(x)=(x^2+4x+4)-5

Answer 6

yes, but you also have to factor x² + 4x + 4

Answer 7

oh I got it. But can you help me with a few others?

Answer 8

ok

Answer 9

Using the completing-the-square method, find the vertex of the function f(x) = –2x2 + 12x + 5 and indicate whether it is a minimum or a maximum and at what point.

Answer 10

\(f(x)=-2x^2+12x+5\)

Group it again
\(f(x)=(-2x^2+12x)+5\)

This time, because you have -2 in front of x², you have to factor it out. Can you do that?

Answer 11

would it be f(x)=-2(x^2+12x)+5

Answer 12

no, you have to divide 12 by -2 as well because it's also in parentheses

Answer 13

so it would be 6?

Answer 14

12/(-2)= -6
So you have
\[f(x)=-2(x^2-6x)+5\]
Now take the coefficient of x, that's -6. Divide it by 2, the square the result like we did above

Answer 15

okay so would it be minimum or maximum?

Answer 16

the number in front of x² is negative, so it's a maximum

Answer 17

okay so whats the point? (-3,5)?

Answer 18

You have to complete the square to find the point

Answer 19

If you don't want to do it that way, use
\[x=-\frac{ b }{ 2a }\]

Answer 20

okay I just reset my exam so now I have different questions

Answer 21

ughhhh I need help