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 − ___
Stacey Warren - Expert brainly.com
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let us consider the blank be a
so y=-16 given
and x = -2
so a = 16+4 -8
you can cross check by solving it.......
so y = x^2+4x-12
@CeCenicole16 have u understand
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.
BTW Dont worry about the x intercept part. Cuzz just finding the vertext at
-2,-16 also takes care of the wanted intercepts :)