# How do you use the important points to sketch the graph of f(x)= -x^2-6x-5?

Mar 19, 2016

Find the x and y intercepts and the vertex and plot these the gradient is negative as ${x}^{2}$ is negative so the graph will be n-shaped

#### Explanation:

Find the x intercepts, factorize
y = $- {x}^{2} - 6 x - 5$
y = $- 1 \left(x + 1\right) \left(x + 5\right)$
when y = 0
x = -1 and x = -5

Find the vertex
The graph is symmetric so the x co-ordinate of the vertex is at the midpoint of the x intercepts
so x = $\frac{- 1 - 5}{2}$ = -3
When x = -3
y = $- \left(- {3}^{2}\right) - \left(6 \times - 3\right) - 5$ = -9 +18 - 5 = 4
So the vertex is at (-3, 4)

Find the y intercept
When x = 0 y = -5

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