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
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)
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)
(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)
Hello! I can help you find the root of the equation y = -x^2 - 2x + 8. To find the roots, you need to solve for x when y = 0, because the roots of an equation represent the x-values where y equals zero.
To solve the equation -x^2 - 2x + 8 = 0, you can use the quadratic formula or factorization method. Here, let's use the quadratic formula:
The quadratic formula is x = (-b ± √(b^2 - 4ac)) / 2a, where a, b, and c are the coefficients of the equation ax^2 + bx + c = 0.
Comparing the equation -x^2 - 2x + 8 = 0 with ax^2 + bx + c = 0, we have:
a = -1, b = -2, and c = 8.
Substituting these values into the quadratic formula, we get:
x = (-(-2) ± √((-2)^2 - 4(-1)(8))) / (2(-1))
Simplifying further:
x = (2 ± √(4 + 32)) / (-2)
x = (2 ± √36) / (-2)
x = (2 ± 6) / (-2)
Now, we have two possible solutions for x:
1. x = (2 + 6) / (-2) = 8 / (-2) = -4
2. x = (2 - 6) / (-2) = -4 / (-2) = 2
So, the roots of the equation y = -x^2 - 2x + 8 are x = -4 and x = 2.
Please note that without the exact graph, I cannot confirm if these roots fall on the provided graph. Make sure to double-check the graph to verify the accuracy of the roots.