How do you use the important points to sketch the graph of f(x)=−x2−6x−5?

1 Answer
Barbara
Mar 19, 2016

Find the x and y intercepts and the vertex and plot these the gradient is negative as x2 is negative so the graph will be n-shaped

Explanation:

Find the x intercepts, factorize
y = −x2−6x−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 = −1−52 = -3
When x = -3
y = −(−32)−(6×−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]}

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