Find the roots of the parabola: y = x 2 +6

Step-by-step explanation:

Firstly, complete the square to put the equation in vertex form,

y

=

−

(

x

+

3

)

2

+

1

This implies that the vertex, or local maximum (since this is a negative quadratic) is

(

−

3

,

1

)

. This can be plotted.

The quadratic can also be factorised,

y

=

−

(

x

+

2

)

(

x

+

4

)

which tells us that the quadratic has roots of -2 and -4, and crosses the

x

a

ξ

s

at these points.

Finally, we observe that if we plug

x

=

0

into the original equation,

y

=

−

8

, so this is the

y

intercept.

All of this gives us enough information to sketch the curve:

graph{-x^2-6x-8 [-10, 10, -5, 5]}