Question

A quadratic function is given.
f(x) = −x^2 − 4x + 4

(a) Express the quadratic function in standard form.

f(x) = ?

Answer 1

This needs to be in form to find the vertex. But I'm lost on how to do this.

Answer 2

for finding vertex, standard form is not necessary.
@hartnn am i correct?

Answer 3

since it need to be in the form of vertex, it should be like f(x)=a(x-h)^2+k
then vertex is (h,k)

Answer 4

so complete the square....

Answer 5

Yeah. I just don't know how to convert it from this form to f(x) = a(x-h)^2+k

Answer 6

factor out -1, u get -1(x^2+4x-4)
now half the middle term like divide the co-efficient of x by 2
what u get ?

Answer 7

or can we use direct formula of vertex (-b/2a , -D/4a)

Answer 8

4/2 = 2

2^2=4 (square it, correct?)

Answer 9

yes,
now add and subtract 4 in that function

Answer 10

-1(x^2+4x -4 +4) -4

?

Answer 11

umm, almost...
-1((x^2+4x +4) -4 -4)
got it ?

Answer 12

i just rearranged the terms and put the brackets

Answer 13

Yes! Makes sense. So would it be: -1(x+2)^2-8

?

Answer 14

be careful with signs
-1((x+2)^2-8 )
-1(x+2)^2+8

Answer 15

How are you getting positive 8? are you distributing?

Answer 16

yes, i need 'k' separate
so i distributed -1

Answer 17

Oh! ok. Thank you very much!

Answer 18

welcome ^_^