Question

the x-intercepts of a quadratic function are -3 and 5. What is the equation of its axis of symmetry??

Answer 1

Remember that when your looking at a quadratic equation, you are looking at a parabola. What is the axis of symmetry in a parabola?

Answer 2

the axis of symmetry is the vertical line that divides the parabola

Answer 3

Exactly. So what will your formula then look like and where will it be located?

Answer 4

well the formula is x=-b/2a...and its an x coordinate

Answer 5

Pardon me, I mean what is the formula for the line that splits a parabola.

Answer 6

The important part here is to understand that the equation for the parabola does not matter, but the symmetry of the parabola proves that it will always hit the x axis at exactly 2 points, of which both are an even number of units away from the axis of symmetry.

Answer 7

Does that help?

Answer 8

sorta...

Answer 9

Alright. Imagine we have a parabola. We move the entirety of the lines to the right, that means the whole parabola moves to the right. The axis of symmetry, which splits it down the middle, should also move correct?

Answer 10

the question im trying to answer is multiple choice...
a. x=-3
b. x=1
c. x=5
d. x=-15

Answer 11

yes correct

Answer 12

So then the axis of symmetry should always be exactly in between the points where it touches the axis correct?

Answer 13

x-axis.

Answer 14

yes

Answer 15

i just don't know how to find that lol

Answer 16

Find the middle point between your two x points, and you will have the x point at y = 0. But we know the symmetry equation should be x = ?. And knowing that x =? is a straight line up and down we should be able to use the point that we found before.

Answer 17

A good way to find the middle point is always to add up the two points, and divide by 2. So (5+(-3))/2.

Answer 18

Is this helping you to understand?

Answer 19

ya for sure!....based on what you told me i got my final answer to be x=1..is that correct?

Answer 20

That is correct. Because the graph is shifted, and we know where it touches x, we don't need to use the formula but rather know that is symmetrical at the line between the x points where it touches. Good job following me I know it can be hard keep it up!

Answer 21

lol well i appreciate any help i can get! thank you sooo much this makes so much more sense now:)

Answer 22

would you mind helping me with one more question?

Answer 23

What is the quation?

Answer 24

well i just want to know how you would find the x intercepts if you were given the solutions to a quadratic equation...so basically the reverse

Answer 25

Like? If it gave you the solutions.. for example.. (x-5)(x+2) which is the parabola x^2-3x-10. You set x-5=0 and x-2=0 and solve for x and those are your two points.

Answer 26

Or you could use the multiply out your solutions and use your formula using the b component.

Answer 27

well the question is ....the solutions to a quadratic equation are x=2 or x=3. what are the x intercepts of the related quadratic function

Answer 28

What is the relation between the functions?

Answer 29

Do you want to find the quadratic they are from or a related one?

Answer 30

related

Answer 31

at least thats what the question says haha

Answer 32

Are the questions in order?

Answer 33

in order?

Answer 34

im sorry english is not my first language

Answer 35

I think I understand the question now. It should relate to the problem we solved before correct? Where the points of the quadratic were x = -3 and x = 5.

Answer 36

What are the answers?

Answer 37

no....its ment to be different....the exact question that im looking at is the solutions to a quadratic equation are x=2 or x=-3. What are the x-intercepts of the related function
a. 2 and -3
b. -1 only
c. -2 and 3
d. -6 and 6

Answer 38

Ok so this is relative to the other solutions. First you should solve for the quadratic, then you should look and see how you can manipulate the equation to come up with a pair of x coordinates that fits.

Answer 39

Does that make sense?

Answer 40

yes

Answer 41

thank you for your help!

Answer 42

For example, could the x components only be -1?

Answer 43

Anytime. good luck!