Question

AN/MEDAL/TESTIMONY
Quadratic Equations

Answer 1

What is the equation of the axis of symmetry if the x-intercepts are (-4,0) and (10,0)?
Explanation please! Thank you! ^u^

Answer 2

what is half way between \(-4\) and \(10\)?

Answer 3

which is another way of asking "what is the average of -4 and 10?"

Answer 4

Half way between -4 and 10? I don't understand, but I would think it's somewhere around the number 5?

Answer 5

somewhere around that yes, but not there

Answer 6

same as saying what is \[\frac{-4+10}{2}\]

Answer 7

Here it is x = -3

Answer 8

This would be the answer the teacher would be looking for!

Answer 9

Oh! Well thank you, but I need an explanation too!

Answer 10

careful here

Answer 11

just because the roots are \(10\) and \(-4\) dots not mean the quadratic is \[(x-10)(x+4)\]

Answer 12

but it does mean the axis of symmetry is half way between those two roots
since the average of \(10\) and \(-4\) is \[\frac{10-4}{2}=3\] that means the axis of symmetry is \(x=3\)

Answer 13

Okay Since we know the x-intercepts as -4 and 10
We can replug it back into the factor form,
x=-4 this becomes (x+4)
and x=10 becomes (x-10)

we take (x+4) multiply by (x-10)

we now get the quadratic equation
Take the quadratic equation into the form ax^2 + bx +c
Use the formula for axis of symmetry as x = b/2a

Answer 14

@satellite73 We only are certain its a quadratic when we multiply them out

Answer 15

it might be \[(x+4)(x-10)\] but it also might be \[2\pi(x+4)(x-10)\]

Answer 16

and we are certain it is a quadratic because they say it has to roots and an axis of symmetry

Answer 17

*two roots

Answer 18

Yeup

Answer 19

Oh! Thank you!