Question

help cause why not? :)



please




What is the axis of symmetry for f(x) = 2x2 − 8x + 8?

x = −2

x = −3

x = 3

x = 2

Answer 1

i can help!

Answer 2

:D @IMStuck that would help :D

Answer 3

you solve it like this, basically to find the vertex. Watch, ok?

Answer 4

\[y=2x ^{2}-8x+8\]to start. Then factor out a 2 so the leading coefficient on the x^2 term is 1.\[y=2(x ^{2}-4x+4)\]

Answer 5

Then put the x terms inside a set of parenthesis and leave the +4 hanging out outside. Like this:\[y=2(x ^{2}-4x)+4\]We did this so we can complete the square on the x terms to find the x coordinate (the line of symmtry) of the vertex.

Answer 6

complete the square by taking half the x term, squaring it, adding it in to the parenthesis and at the same time subtracting it out, like this:\[y=2(x ^{2}-4x+4-4)+4\]

Answer 7

half of -4 is -2, (-2)^2 is 4. Get that?

Answer 8

now we need to move the -4 out of the parenthesis and add it to the +4 hanging out there, but keep in mind that while that -4 was inside the parenthesis, it was being multiplied by the 2 out front. So when you take out the -4, you need to bring the 2 with it, like this:\[y=2(x ^{2}-4x+4)+(-4)(2)+4\]

Answer 9

This comes out to\[y=2(x ^{2}-4x+4)-4\]

Answer 10

now make a perfect square binomial out of what is inside the parenthesis, remembering what you originally squared to get the 4 you added in (it was a 2). So the equation now is\[y=2(x-2)^{2}-4\]

Answer 11

From this you can add the 4 to the other side to find the y coordinate of the vertex (-4), but the line of symmetry is found by setting (x-2) equal to zero and solving for x.
If x-2=0, then x=2. That's your line of symmetry. It is also your x coordinate for your vertex which is (2, -4)

Answer 12

x=2 is your answer.

Answer 13

thanks dude @IMStuck