Question

9.03] Part 1 − Find the vertex, axis of symmetry, domain, and range of the graph of y = −4x2 + 4x − 7. Show all work for full credit. Part 2 − Using complete sentences, explain how you can determine the axis of symmetry, the domain, and range without graphing y = −4x2 + 4x − 7.

Answer 1

do u know how to complete squares?

Answer 2

no

Answer 3

let's try it to together then: u have
\[ \large y=-4x^2+4x-7 \]
then
\[ \large y+7=-4(x^2-x+\qquad) \]
ok so far?

Answer 4

no why did you put x^2 and -x

Answer 5

first i added +7 to both sides.
then i factored -4 from what was left on the right hand side
ok?

Answer 6

ohhh ok

Answer 7

now the coeficent of x^2 is 1 and the coefficient of x is -1.
in order to get a perfect square we have to put a number in the blank i left.
this number is the coefficient of x halved and then squared.
do u get this?

Answer 8

ok, yes i get it

Answer 9

now we write:
\[ \large y+7\color{red}{-4\cdot\left(\frac{-1}{2}\right)^2}
=-4\left(x^2-x+\color{red}{\left(\frac{-1}{2}\right)^2}\right) \]

Answer 10

got it?

Answer 11

hello?? @valentinapaez

Answer 12

well u finalli get
\[ \large y+6=-4(x-1/2)^2 \]

Answer 13

i hope i was of help.

sorry. but i gotta go

Answer 14

wait