U4D2 Intro to Graphing Polynomial Functions Mar6

Instructions

In this lesson we will practice skills to help us graph polynomial functions.

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Review Inputs/Outputs for Linear Equations
Complete the T-Chart to find coordinates and use the coordinates to graph the line.

1

Review Inputs/Outputs for Linear Equations
Complete the T-Chart to find coordinates and use the coordinates to graph the line.

1

Review Inputs/Outputs for Linear Equations
Complete the T-Chart to find coordinates and use the coordinates to graph the line.

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Evaluate Functions From a Graph
Use the graph to find the value of y when x = 3.

f(3) = _______ 

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Evaluate Functions From a Graph
Use the graph to find the value of y when x = -5.

f(-5) = _______ 

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Input vs. Output on a Graph

f(6) = _______ 

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Input vs. Output on a Graph

x = _______ , when f(x) = 4.

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Input vs. Output on a Graph

x = _______ , when f(x) = 0.

VOCABULARY

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The function f(x) is graphed below. How many points on the graph represent a relative minimum?

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The function f(x) is graphed below. How many points on the graph represent a relative extrema?

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Identify the graph that represents a quadratic function:

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Which of the following is an example of a quadratic function?

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What is the axis of symmetry of a quadratic function?

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The equation 𝑦 = (𝑥 − 2)2 represents a quadratic function.
What is the vertex of this function?

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Which is NOT a possible number of solutions to a quadratic equation?

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Which of the following represents a quadratic function in standard form?

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What is the shape of the graph of a quadratic function?

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Which of the following is NOT a characteristic of a quadratic function?

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A ball is thrown into the air with an initial velocity of 30 meters per second. The height of the ball (in meters) can be modeled by the quadratic function ℎ(𝑡) = −5𝑡 2 + 30𝑡 + 5, where t represents time in seconds. Determine the maximum height the ball reaches and the time it takes to reach that height.

Solution:
The maximum height would be _______  meters at _______  seconds.

1

A model rocket is launched from the ground with an initial velocity of 40 meters per second. The height of the rocket (in meters) above the ground after 𝑡 seconds is given by the function ℎ(𝑡) = −5𝑡 2 + 40𝑡. 

a. Determine the maximum height the ball reaches and the time it takes to reach that height.

Solution:
The maximum height would be _______  meters at _______  seconds.

b. Determine the time it takes for the rocket to reach the ground after being launched.

Solution:
The rocket will return to the ground at _______  seconds.

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A ball is thrown off a cliff with an initial velocity of 25 meters per second. The height of the ball (in meters) above the ground after 𝑡 seconds is given by the function
ℎ(𝑡) = −4.9𝑡 2 + 25𝑡 + 20. (Round answers to the nearest tenth.)

a. Determine the maximum height the ball reaches and the time it takes to reach that height. (Round answers to the nearest tenth.)

Solution:
The maximum height would be _______  meters at _______  seconds.

b. Determine the time it takes for the rocket to reach the ground after being launched. (Round answers to the nearest tenth.)

Solution:
The rocket will return to the ground at _______  seconds.

1

A farmer is constructing a rectangular pen for his animals. He wants to enclose a total area of 200 square meters using one side of the pen as a barn wall. The width of the pen (in meters) is represented by the quadratic function 𝑤(𝑥) = 𝑥 2 − 6𝑥 + 8, where x represents the length of the pen. Determine the dimensions of the pen that will maximize the width.
(Round your answers to the nearest tenth.)

Solution:
The length of the pen is _______  meters.
The width of the pen is _______  meters.

U4D2 Intro to Graphing Polynomial Functions Mar6

Review Inputs/Outputs for Linear EquationsComplete the T-Chart to find coordinates and use the coordinates to graph the line.

Review Inputs/Outputs for Linear EquationsComplete the T-Chart to find coordinates and use the coordinates to graph the line.

Review Inputs/Outputs for Linear EquationsComplete the T-Chart to find coordinates and use the coordinates to graph the line.

The function f(x) is graphed below. How many points on the graph represent a relative minimum?

The function f(x) is graphed below. How many points on the graph represent a relative extrema?

Identify the graph that represents a quadratic function:

Which of the following is an example of a quadratic function?

What is the axis of symmetry of a quadratic function?

The equation 𝑦 = (𝑥 − 2)2 represents a quadratic function. What is the vertex of this function?

Which is NOT a possible number of solutions to a quadratic equation?

Which of the following represents a quadratic function in standard form?

What is the shape of the graph of a quadratic function?

Which of the following is NOT a characteristic of a quadratic function?

Review Inputs/Outputs for Linear EquationsComplete the T-Chart to find coordinates and use the coordinates to graph the line.

Review Inputs/Outputs for Linear EquationsComplete the T-Chart to find coordinates and use the coordinates to graph the line.

Review Inputs/Outputs for Linear EquationsComplete the T-Chart to find coordinates and use the coordinates to graph the line.

The function f(x) is graphed below. How many points on the graph represent a relative minimum?

The function f(x) is graphed below. How many points on the graph represent a relative extrema?

Identify the graph that represents a quadratic function:

Which of the following is an example of a quadratic function?

What is the axis of symmetry of a quadratic function?

The equation 𝑦 = (𝑥 − 2)2 represents a quadratic function. What is the vertex of this function?

Which is NOT a possible number of solutions to a quadratic equation?

Which of the following represents a quadratic function in standard form?

What is the shape of the graph of a quadratic function?

Which of the following is NOT a characteristic of a quadratic function?

Review Inputs/Outputs for Linear Equations
Complete the T-Chart to find coordinates and use the coordinates to graph the line.

Review Inputs/Outputs for Linear Equations
Complete the T-Chart to find coordinates and use the coordinates to graph the line.

Review Inputs/Outputs for Linear Equations
Complete the T-Chart to find coordinates and use the coordinates to graph the line.

The equation 𝑦 = (𝑥 − 2)2 represents a quadratic function.
What is the vertex of this function?

Review Inputs/Outputs for Linear Equations
Complete the T-Chart to find coordinates and use the coordinates to graph the line.

Review Inputs/Outputs for Linear Equations
Complete the T-Chart to find coordinates and use the coordinates to graph the line.

Review Inputs/Outputs for Linear Equations
Complete the T-Chart to find coordinates and use the coordinates to graph the line.

The equation 𝑦 = (𝑥 − 2)2 represents a quadratic function.
What is the vertex of this function?