Integrated Mathematics II - Tripod



Quadratic Functions – Review

There are basically 3 different forms/types of quadratic functions, in terms of how they look:

|Form/Type |What it Looks Like |

|Standard Form |[pic] |

|Factored Form |[pic] |

|Vertex Form |[pic] |

The two major concepts from the Quadratics unit are:

• Solving quadratic equations written in any of the above forms

• Graphing quadratic equations written in any of the above forms

Then these concepts have lots of applications associated with them, such as finding a maximum or minimum value, finding a point where a person’s height is 0 m above the water, etc., etc. –these applications involve understanding the solutions and graphs that you get.

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Solving Quadratic Equations

Solve the following for x:

1) [pic] 2) [pic]

3) [pic] 4) [pic]

5) [pic] 6) [pic]

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Graphing Quadratic Equations

1) Complete this table to help you in your review:

|Form/Type |What it Looks Like |How to find |How to find y-intercept|How to find x- coord.|How to find y-coord of |

| | |x-intercepts | |of vertex (axis of |vertex |

| | | | |symmetry) | |

|Standard Form |[pic] | | | | |

|Factored Form |[pic] | | | | |

|Vertex Form |[pic] | | | | |

2) For the function [pic], find the vertex, the x-intercepts, and the y-intercept. (You may want to find them in a different order from what’s listed…or maybe not… ()

vertex: ___________

x-intercepts: ___________

y-intercept: ___________

3) For the function [pic], find the vertex, the x-intercepts, and the y-intercept.

(You may want to find them in a different order from what’s listed…or maybe not… ()

vertex: ___________

x-intercepts: ___________

y-intercept: ___________

4) For the function [pic], find the vertex, the x-intercepts, and the y-intercept.

(You may want to find them in a different order from what’s listed…or maybe not… ()

vertex: ___________

x-intercepts: ___________

y-intercept: ___________

5) How many x-intercepts does the graph of [pic] have? (No calculator – show all work.)

6) A stone was thrown from the top of a cliff 60 metres above sea level. The height of the stone above sea level t seconds after it was released is given by [pic].

[If you use a calculator to answer the following questions, sketch a graph here with key points labeled]:

a) How long does it take for the stone to reach its maximum height?

b) What was the maximum height above sea level that the stone reached?

c) How long did it take before the stone struck the water?

7) Mr. Smith’s science class is having a contest. Each student shoots their toy rocket into the air from ground level, and they see which rocket stays in the air longest, according to Mr. Smith’s digital stopwatch. For this situation, we will assume that the height of the rocket as time passes is a quadratic relationship. We will let y represent height (in feet) above the ground, and x represent seconds since the stopwatch was started. Here’s what we know about some of the rockets:

• John’s rocket is shot into the air as the stopwatch is started, and lands 3.2 seconds later.

• Julia doesn’t get her rocket in the air until 4.5 seconds after the stopwatch is started, and it lands when the stopwatch reads 7.3 seconds. She estimates her rocket goes up to a height of 31 ft.

• The height of Donna’s rocket can be described by this equation: [pic]

Use this information to answer the following questions.

a) Write an equation of the height of John’s rocket as time passes, in factored form, [pic], given that [pic]. (So,[pic]; you find b and c and write them into the equation.)

b) At what time on the stopwatch did Julia’s rocket reach its maximum height?

c) Draw a graph of the height of Julia’s rocket, as time passes. Be sure to label the axes carefully. Also, label any key points that you know.

d) At what time on the stopwatch did Donna shoot her rocket, and at what time did it land?

e) Of John’s, Julia’s, and Donna’s rockets, whose stayed in the air the longest? Explain your thinking.

f) Wishing for extra credit, Donna thinks about climbing onto the school roof (30 feet high) and launching her rocket from its edge, so that it lands on the ground. Circle the correct choice for how this affects the time Donna’s rocket is in the air.

The time in the air of Donna’s rocket would be less / the same / greater if she shot it from the roof and it landed on the ground.

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