Algebra 1 Unit 3C – Graphing Quadratics

Name: ________________________________________________ Date: _______________________Quadratics Modeled in the Real World

Philip is standing on a rock ledge 64 feet above a lake, and he tosses a rock with a velocity of 48 feet per second. This graph and table represent the height above the water, h(t), as a function of time, t, in seconds after Philip releases the rock.

1. What is the maximum height of the rock?

2. After how many seconds does the rock change direction in the air?

3. How can you estimate the maximum height from the table?

4. When does the rock hit the surface of the lake? What is this point on the graph called? How can you identify this from the table?

5. Identify the vertex and the axis of symmetry. What do these represent in our story?

6. At 1 sec, what direction is the rock moving? At 2 sec, what direction is the rock moving?

Philip is standing on a rock ledge 64 feet about a lake, and he tosses a rock with a velocity of 48 feet per second.

7. Using , write an equation in standard form for the path of the rock.

Time t Height h(t)0 641 962 963 644 0

Algebra 1 Unit 3C – Graphing Quadratics

8. Will this graph open up or down? Will the vertex be a maximum or a minimum? Why?

9. Using your standard form equation from #1, write the equation in vertex form (decimals are ok).

10. Using the equation from #9, what is the maximum height the rock reaches above the surface of the lake? How did you get this answer?

11. Using the equation from #9, after how many seconds did the rock change direction in the air? How did you get this answer?

12. At 1 sec, what direction is the rock moving? At 2 sec, what direction is the rock moving?

A frog is about to hop from the bank of a creek. The path of the jump can be modeled by the equation h ( x )=−x2+4 x+1, where h(x) is the frog’s height above the water and x is the number of seconds since the frog jumped. A fly is cruising at a height of 5 feet above the water.

13. Can the frog catch the fly without jumping? How do you know?

14. Is the extrema a maximum or minimum? Why?

15. What is the vertex of the equation?

16. If the frog jumps to catch the fly, is it possible for the frog to catch the fly?