Question

Find the vertex of the given parabola. Please show work.
y=-x^2-2x+9

Answer 1

vertex = -b/2a = -(-2) / 2(-2) = -1

Answer 2

^^ gives you the x-coordinate of vertex
Substitute that value into equation to find y-coordinate

Answer 3

The standard equation of a parabola is

y = ax2 + bx + c.

"vertex form":

y = a(x – h)2 + k

a= -1 b =2

-b/2a

2/2(-1)

= -1 the x-coordinate of the vertex.

Substituting in the original equation to get the y-coordinate, we get:

y= -x^2 - 2x +9

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

= 12

So, the vertex of the parabola is at

(-1 , 12)

Answer 4

Watch the signs:
-x^2 = -(x^2)
x = -1
-(-1)^2 = -1
-1-2(-1) + 9 = -1 + 2 +9 = 10

vertex: (-1,10)