Lesson 11

Graphing from the Factored Form

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Problem 1

Select all true statements about the graph that represents \(y=2x(x-11)\).

A:

Its \(x\)-intercepts are at \((\text-2,0)\) and \((11,0)\).

B:

Its \(x\)-intercepts are at \((0,0)\) and \((11,0)\).

C:

Its \(x\)-intercepts are at \((2,0)\) and \((\text-11,0)\).

D:

It has only one \(x\)-intercept.

E:

The \(x\)-coordinate of its vertex is -4.5.

F:

The \(x\)-coordinate of its vertex is 11.

G:

The \(x\)-coordinate of its vertex is 4.5.

H:

The \(x\)-coordinate of its vertex is 5.5.

Solution

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Problem 2

Select all equations whose graphs have a vertex with \(x\)-coordinate 2.

A:

\(y=(x-2)(x-4)\)

B:

\(y=(x-2)(x+2)\)

C:

\(y=(x-1)(x-3)\)

D:

\(y=x(x+4)\)

E:

\(y=x(x-4)\)

Solution

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Problem 3

Determine the \(x\)-intercepts and the \(x\)-coordinate of the vertex of the graph that represents each equation. 

equation \(x \)-intercepts \(x\)-coordinate of the vertex
\(y=x(x-2)\)    
\(y=(x-4)(x+5)\)    
\(y= \text-5x (3-x)\)    

Solution

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Problem 4

Which one is the graph of the equation \(y=(x-3)(x+5)\)?

Graph A

Graph of non linear function.

Graph B

Graph of non linear function, origin O. Horizontal axis from negative 8 to 6, by 2’s. Vertical axis from negative 8 to 12, by 4’s. Line passes through 1 comma 7, 3 comma 0, 5 comma 0, and 7 comma 7.

Graph C

Graph of non linear function.

Graph D

Graph of non linear function, origin O. Horizontal axis from negative 8 to 6, by 2’s. Vertical axis from negative 16 to 4, by 4’s. Line passes through negative 3 comma 0, 1 comma negative 16, and 5 comma 0.
A:

Graph A

B:

Graph B

C:

Graph C

D:

Graph D

Solution

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Problem 5

  1. What are the \(x\)-intercepts of the graph of \(y=(x-2)(x-4)\)?
  2. Find the coordinates of another point on the graph. Show your reasoning.
  3. Sketch a graph of the equation \(y = (x-2)(x-4)\).

Solution

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Problem 6

A company sells calculators. If the price of the calculator in dollars is \(p\), the company estimates that it will sell \(10,\!000-120p\) calculators.

Write an expression that represents the revenue in dollars from selling calculators if a calculator is priced at \(p\) dollars.

Solution

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(From Unit 6, Lesson 7.)

Problem 7

Is \((s+t)^2\) equivalent to \(s^2+2st+t^2\)? Explain or show your reasoning.

Solution

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(From Unit 6, Lesson 8.)

Problem 8

Tyler is shopping for a truck. He found two trucks that he likes. One truck sells for $7,200. A slightly older truck sells for 15% less. How much does the older truck cost?

Solution

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(From Unit 5, Lesson 14.)

Problem 9

Here are graphs of two exponential functions, \(f\) and \(g\).

The function \(f\) is given by \(f(x) = 100 \boldcdot 2^x\) while \(g\) is given by \(g(x) = a \boldcdot b^x\).

Based on the graphs of the functions, what can you conclude about \(a\) and \(b\)?

2 exponential functions.

Solution

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(From Unit 5, Lesson 13.)

Problem 10

Suppose \(G\) takes a student’s grade and gives a student’s name as the output. Explain why \(G\) is not a function.

Solution

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(From Unit 4, Lesson 2.)