5.1.2 Properties of Quadratic Functions in Standard Form - Worksheet
Example 1: Identify the axis of symmetry for the graph of each function. 1. f ( x ) = − 2( x − 2) 2 − 4 2. g ( x ) = 3 x 2 + 4
3. h ( x ) = ( x + 5) 2
Example 2: For each function, (a) determine whether the graph opens upward or downward,
(b) find the axis of symmetry,
(c) find the vertex,
(d) find the y -intercept, and
(e) graph the function.
4. f ( x ) = − x 2 − 2 x − 8
5. g ( x ) = x 2 − 3 x + 2
6. h ( x ) = 4 x − x 2 − 1
Example 3: Find the minimum or maximum value of each function. Then state the domain and range of the function. 7. f ( x ) = x 2 − 1 8. g ( x ) = − x 2 + 3 x − 2 9. h ( x ) = − 16 x 2 + 32 x + 4
Example 4: 10. The path of a soccer ball is modeled by the function h ( x ) = − 0.005 x 2 + 0.25 x , where h is the height in meters and x is the horizontal distance that the ball travels in meters. What is the maximum height that the ball reaches?
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