Example #2
The function is graphed below f(x) = -2x2 - 4x -4. Identify the key features of the graph.
Is this a positive or negative parabola?
Answer: This is a negative parabola because it is opening down. You also know this is a negative parabola because the value of a is -2 which is less than 0.
What is the vertex of the function?
(___, ___)
Answer: (-1, -2)
What is the equation for the Axis of Symmetry?
x = ___
Answer: x = -1
What is the maximum or minimum point for the graph? Because this graph opens down, you will only have a maximum value. The maximum value occurs at the vertex. The maximum value is (-1, -2).
Where is the graph increasing? The graph begins increasing at an indefinite x-value and continues to an x-value of -1. The interval will be (-∞ , -1).
Where is the graph decreasing? The graph begins decreasing at an x-value of -1 and continues to the right indefinitely. The interval will be (-1, ∞ ).
What are the x-intercepts of the graph? There are no x-intercepts to this graph because the graph does not intersect the x-axis.
What is the y-intercept of thegraph?
(0, ___ )
Answer: (0, -4)
The graph below is the graph of f(x) = -2x2 – 4x – 4.
Summary of the Key Features
Negative Parabola
Vertex: (-1, -2)
Axis of Symmetry: x = -1
Increasing: (- ∞, -1)
Decreasing: (-1, ∞ )
Minimum Value: (-1, -2)
x-intercepts: None
y-intercept: (0, -4)
