Question

What are the zeroes of f(x) = x2 - 6x + 8? (4 points)

x = -4, 2
x = -4, -2
x = 4, 2
x = 4, -2

Answer 1

help!!

Answer 2

Hello!
sorry for the kinda slow reply .-.

do you know how to factor?
aka backwards FOILing?

Answer 3

yes i know how to foil

first
outers
inners
last

Answer 4

that's good :)

but now we have to do it backwards

for example

x^2 - 8x + 12
= (x)(x) - (6x) - (2x) + (6)(2)
= (x - 6)(x - 2)

Answer 5

ok

Answer 6

can you walk me through it please?

Answer 7

of course :)

first we have to understand that in our equation: \( x^2-6x+8 \)
we have to find two numbers (x + #)(x + #)
that will go here ^ ^

these two numbers should \(multiply~up~to~positive~8\)
and \(add~up~to~negative~6\)

Answer 8

so let's first list the pairs of numbers that can multiply up to a positive 8 :)

Answer 9

ok

Answer 10

this would include
\( 1~and~8 \)
\( -1~and~-8\)

etc

can you find a pair that adds up to \(-6\) ?

[adds up like \(-1 + -8 = -9\) ]

Answer 11

ok i see

Answer 12

1 and 8
-1 and -8
2 and 4
-2 and -4

1+8=9
-1 + -8 = -9
2+4= 6
-2 + -4 = -6 <-- so the pair of -2 and -4 works

Answer 13

all we have to do now is to plug "-2" and "-4"
into (x + __)(x + __)
^ ^
to have our factored version of the equation

Answer 14

\(Warning!\) Don't select an answer yet!

Answer 15

(x - 2)(x - 4)

now the "zeros" of this would be when each part is set equal to "zero"

x - 2 = 0 [solve for x]

x - 4 = 0 [solve for x]

noww you will get your answers :)