Question

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

Answer 1

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 -6x -5`
y = `-1(x +1)(x +5)`
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 = `(-1 - 5)/2` = -3
When x = -3
y = `-(-3^2) - (6xx-3) -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]}