Example #1
The graph below is f(x) = x2 + 8x + 12. Identify the key features of the graph.
Is this a positive or negative parabola?
Answer: This is a positive parabola because it is opening up. You also know this is a positive parabola because the value of a is 1 which is greater than 0.
What is the vertex of the function?
( ___ , ___ )
Answer: (-4, -4)
What is the equation for the axis of symmetry?
x = ___
Answer: x = -4
What is the maximum or minimum point for the graph? Because this graph opens up, you will only have a minimum value. The minimum value occurs at the vertex. The minimum value is the same as the vertex, (-4, -4).
Where is the graph increasing?
The graph begins increasing at an x-value of -4 and continues to the right indefinitely. The interval will be (-4, ∞). Hint! Always remember that graphs continue indefinitely to the left and to the right. When indicating "indefinitely" in math terms, you will use the infinity symbol (∞). You can have one of two possibilities for your intervals of increasing and decreasing: (x, ∞) or (-∞, x). x represents the x-coordinate of the vertex.
Where is the graph decreasing?
The graph begins decreasing at an indefinite x-value and continues to an x-value of -4. The interval will be (-∞, -4).
What are the x-intercepts of the graph?
( __ , 0)
( __ , 0)
Answer:
(-6, 0)
(-2, 0)
What is the y-intercept of the graph?
(0, ___ )
Answer: (0, 12)
The graph below is f(x) = x2 + 8x + 12.
Summary of the Key Features
Positive Parabola
Vertex: (-4, -4)
Axis of Symmetry: x = -4
Increasing: (-4, ∞ )
Decreasing: (-∞ , -4)
Minimum Value: (-4, -4)
x-intercepts: (-6, 0) and (-2, 0)
y-intercept: (0, 12)
