Question

Hello,
I need help answering a regents question. It is asking me to find the root of an equation. It also includes a graph which I am unable to upload.The equation is y = −x2 − 2x + 8.
-Thank You

Answer 1

root means what is x when y is zero.

x^2+2x-8=0
what multiplies to -8 and adds to 2?

(x-2)(x+4)=0
x=2, x=-4 two roots.
On the graph, the roots are where it crosses the x axis (y=0)

Answer 2

y = −x^2 − 2x + 8 I assume

Let's look at it by completing the square

x^2 + 2 x = -y + 8

x^2 + 2 x + 1 = -y + 9

(x+1)^2 = -(y-9)

That is a parabola (upside down, sheds water because of the - in front of y) with an axis of symmetry of x = -1 where (x-1) = 0
the vertex is on that axis where x-1 = 0 so when y = 9.
then when y = 0. the "roots":
(x+1)^2= 9
so
x+1 = 3
or
x+1 = -3
so
(2,0) or (-4,0)

Answer 3

(x+1)^2 = -(y-9)

That is a parabola (upside down, sheds water because of the - in front of y) with an axis of symmetry of x = -1 where (x+1) = 0
the vertex is on that axis where x+1 = 0 so when y = 9.
then when y = 0. the "roots":
(x+1)^2= 9
so
x+1 = 3
or
x+1 = -3
so
(2,0) or (-4,0)