Question

what is the axis of symmetry for the equation x= x^2+8x+3 ?

Answer 1

x= or y=?

Answer 2

sorry i meant f(x)=

Answer 3

ah ....

Answer 4

do you know how to find the vertex? or to put this into f(x)=a(x-h)^2+k format?

Answer 5

not really..

Answer 6

hmm, another way of looking at it would be if you know how to find the zeros, or roots, of the equation; the line of symmetry would be the midpoint between the roots .... provided it crosses the x axis to begin with

Answer 7

formula-wise we have:

given: ax^2 + bx + c

the line of symmetry can be determined as:

x = -b/2a

Answer 8

so im going to put -8/ 2(1) ?

Answer 9

thats perfect

Answer 10

oh yay! so i get x=-4?

Answer 11

yes, x=-4 will be the axis of symmetry, good job

Answer 12

so how do i find the vertex?

Answer 13

the vertex actully sits right on the axis of symmetry; so we know x=-4 is the axis; use x=-4 in the equation itself to find the y value that defines the point for the vertex

Answer 14

otherwise we would have to go the route of completing the square .... which isnt difficult, but is rather involved

Answer 15

wait which equation?

Answer 16

x^2+8x+3 the one youre asking about is this one correct?

Answer 17

yes! so i'm going to put -4 in each x?

Answer 18

correct, since we know the x part of the point has to be -4

Answer 19

so one of the points are going to be -4? the x one? & when i plug the -4 into the x's its going to give me the y? am i right or way off?

Answer 20

that is correct.

Answer 21

i got -13 when i plugged in the -4 to all the x's!

Answer 22

so my vertex is (-4, -13) ?

Answer 23

lets see what i get to verify

16-32+3 = -16+3 = -13 yes

Answer 24

correct (-4,-13) is the vertex of this parabola then

Answer 25

okay and since its both negative, the parabola is going to be like...

Answer 26

so minimum!

Answer 27

not quite, the vertex only tells us where the parabola bends at; the direction that it open up towards is determined by looking at the first term of the eqaution; the "ax^2" part

Answer 28

ax^2 is positive so it opens up

-ax^2 is negtaive so it opens down

Answer 29

so its going to be going the other wayy?

Answer 30

given your equation; it starts with: x^2

so it will open the same way as x^2 does: like a U

Answer 31

so thats a maximum?

Answer 32

if your question is whether the vertex is the highest (max) point or the lowest (min) point on the parabola; i would go with lowest since all the other points are moving up and higher than it

Answer 33

it says state whether the vertex is max or min..