Question

Fill in the missing term so that the quadratic equation has a graph that opens up, with a vertex of
(– 2, – 16), and x intercepts at x = -6 and x = 2. (Do not include the negative sign in your answer.)

y = x2 + 4x − ___

Answer 1

let us consider the blank be a
so y=-16 given
and x = -2
therefore
-16=(-2)^2+4(-2)-a
-16=4-8-a
so a = 16+4 -8
=12
you can cross check by solving it.......
so y = x^2+4x-12

Answer 2

@CeCenicole16 have u understand

Answer 3

Here is what you do.

It is asking for a c term a c term just moves it up and down. the graph i mean.

So lets plug in 0 just as a start and a reference point.

x^2 + 4*x
x (x+4) factored form

from that it is easy to tell the roots are 0 and -4. Or you can solve for it however you want.

since the midpoint from 0 to -4 is -2. That tells us the vertex is at -2.

we plug -2 it into x (x+4)=-2*(-2+4)=-4

Vertex at -2,-4.

Remember i said adding a c term just shifts it up and down? That means -2 will stay the same but the y will change.

the vertex is at

-2,-4 for now

They ask for

(– 2, – 16)
^ this dont matter since addinc a c term wont change it.
^ this does adding a c term will change it.

we at -4 and want -16

but keep in mind
y = x2 + 4x − ___ it wants it as a -
Lets set up an equation for that

-4-c=-16 c=12 is answer. BUt lets check

x^2 + 4*x -12 we plugged in 12 for that ___ blank


(-2)^2 + 4*(-2) -12 =-16 we plug in -2


IT works and below is the visual proof.
https://www.google.com/search?q=x%5E2+%2B+4x+ −+0&oq=x%5E2+%2B+4x+−+0&aqs=chrome..69i57j0l3.7250j0&sourceid=chrome&ie=UTF-8#q=(x)%5E2+%2B+4*(x)+-12%2C+(x)%5E2+%2B+4*(x)

BTW Dont worry about the x intercept part. Cuzz just finding the vertext at
-2,-16 also takes care of the wanted intercepts :)

Answer 4

Also dont worry about the opening up part. SInce
x2 + 4x − ___
^ that term takes care of it opening up.

not ^ c term.