Question

how do i find the axis of symmetry of y=x^2-4x=7?

Answer 1

i mean y=x^2-4x+7

Answer 2

This is a quadratic function, so the graph is a parabola. The axis of symmetry passes through the vertex. Do you know a way to find the vertex?

Answer 3

i got (2,14) as the vertex

Answer 4

its probably wrong though.. i did (b/2 , c(4/2) )

Answer 5

well im guessing it would be 4/2 for x and then 7(4/2) for y

Answer 6

Yeah, that doesn't seem to check out.
Looks like you're using the short cut from the quadratic formula, the x-coordinate of the vertex is -b/2a

Answer 7

that's what someone on here told me to do.

Answer 8

so it would be -4/2(1)

Answer 9

It's a quick and reliable method. Here, since you're looking for an equation of the line of symmetry, you don't need the y-coordinate of the vertex, just x=h : h = -b/2a

Answer 10

h = -(-4)/(2(1)) = 2.

Answer 11

i need to find the vertex too though

Answer 12

Don't forget the negative sign. b = -4 not just 4.

Answer 13

Well, then the y-coordinate of the vertex is the function evaluated at y=f(h).

Answer 14

so the line of symmetry is 2? or that's just the x?

Answer 15

i.e. take the x=2 you got for the axis of symmetry and put it into the equation to get y.

Answer 16

The line of symmetry is x=2. You have to include the 'x=' because the line is defined by an equation.

Answer 17

so y=7(2)?

Answer 18

y=(2)^2-4(2)+7. You have to use the whole equation.

Answer 19

i get it now!

Answer 20

hmmm same as before

Answer 21

did you find the vertex?

Answer 22

im doing it right now

Answer 23

ok

Answer 24

y=-1?

Answer 25

Alternate method is to complete the square to put the function in vertex form.

Answer 26

Check your signs . .

Answer 27

notice the "a" component, that is, the leading coefficient is positive, that means is going upwards VERTICALLY, so the symmetry for the vertical one, will be the "x" coordinate of the vertex

Answer 28

so it's not -1, it's positive?

Answer 29

well \(\bf \left(-\cfrac{b}{2a}, c-\cfrac{b^2}{4a}\right)\\
-\cfrac{b}{2a} \implies -\cfrac{-4}{2(1)} \implies 2\)

Answer 30

so it's (2,2)

Answer 31

well, you don't need the y-coordinate, since the axis of symmetry is just the x-coordinate only

Answer 32

ok. and then the vertex would be (2,1)? that's what i got

Answer 33

\(\bf c-\cfrac{b^2}{4a} \implies 7-\cfrac{(-4)^2}{4(1)} \implies 7-\cfrac{\cancel{16}}{\cancel{4}} \implies 7-4\)

Answer 34

so (2,3)?

Answer 35

for the vertex, yes

Answer 36

ok thanks again!

Answer 37

yw