Question

i need to find the vertex of x^2+8x+7

Answer 1

Do you know some calculus?

Answer 2

no im in algebra 1

Answer 3

In that case, start by factoring that polynomial. Can you do that?

Answer 4

yes i got -1 and -7

Answer 5

Now, what is the point between \(-1\) and \(-7\)?

Answer 6

what do you mean?

Answer 7

As soon as you find the two roots, you need to find the midpoint of the segment \([-7,-1]\).

Answer 8

is it the remaining 8 ?

Answer 9

\[\frac{-7+-1}{2}=-4\]

Answer 10

so you start at the negative four?

Answer 11

You know that the vertex of the parabola has an \(x\)-value of \(-4\). What is the \(y\)-value?

Answer 12

-9

Answer 13

That is correct.

Answer 14

Using calculus, you can just differentiate:\[2x+8=0\implies x=-4\implies y=-9.\]

Answer 15

so you mark the point on the graph (-4,-9) ?

Answer 16

That's correct. :)

Answer 17

thank you