Question

The graph models the function y = −x2 − x + 6. Which attribute(s) of the graph tell you the root(s) of the function? Determine the root(s).

Answer 1

Roots are -3, 2

Explanation:

y = −x^2 − x + 6

To find out the roots we set y=0 and solve for x

0 = -x^2 -x+6

Factor out -1

0=-1(x^2+x-6)

divide both sides by -1

x^2 +x -6=0, factor x^2 +x-6

product is -6 and sum +1

3* (-2) = -6

3-2= 1

so factors are 3 and -2

x^2 +x -6=0

(x+3)(x-2)=0

Set each factor =0 and solve for x

x+3 =0 , so x=-3

x-2=0, so x= 2

Roots are -3, 2

Answer 2

In a graph the roots of the function are given by the cut points with the x axis.
On the other hand, we have the following equation:
y = -x2 - x + 6
To find the roots, we equate to zero:
-x2 - x + 6 = 0
Rewriting we have:
x2 + x - 6 = 0
(x-2) (x + 3) = 0
The roots are:
x1 = 2
x2 = -3
Answer:
The roots are:
x1 = 2
x2 = -3