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9-12 Integrated Math 2 Unit 4 Lesson 10

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Unit 4, Lesson 10

Graphs of Functions in Standard and Factored Forms

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Integrated Math 2

Practice

Problem 1

A quadratic function, \(f\), is defined by \(f(x)=(x-7)(x+3)\).

Without graphing, identify the \(x\)-intercepts of the graph of \(f\). Explain how you know.
Expand \((x-7)(x+3)\) and use the expanded form to identify the \(y\)-intercept of the graph of \(f\).

Problem 2

What are the \(x\)-intercepts of the graph of the function defined by \((x-2)(2x+1)\)?

\((2,0)\) and \((\text-1,0)\)
\((2,0)\) and \(\left(\text-\frac12,0\right)\)
\((\text-2,0)\) and \((1,0)\)
\((\text-2,0)\) and \((\frac12,0)\)

Problem 3

Here is a graph that represents a quadratic function.

Which expression could define this function?

<p>A curve in an x y plane, origin O, with grid.</p>

\((x+3)(x+1)\)
\((x+3)(x-1)\)
\((x-3)(x+1)\)
\((x-3)(x-1)\)

Problem 4

What is the \(y\)-intercept of the graph of the equation \(y = x^2 - 5x + 4\)?
An equivalent way to write this equation is \(y = (x-4)(x-1)\). What are the \(x\)-intercepts of this equation’s graph?

Problem 5

Noah said that if we graph \(y=(x-1)(x+6)\), the \(x\)-intercepts will be at \((1,0)\) and \((\text-6,0)\). Explain how you can determine, without graphing, whether Noah is correct.

Problem 6

ForLesson 7: Building Quadratic Functions to Describe Situations (Part 3)

A company sells a video game. If the price of the game in dollars is \(p\), the company estimates that it will sell \(20,\!000 - 500p\) games.

Which expression represents the revenue in dollars from selling games if the game is priced at \(p\) dollars?

\((20,\!000 - 500p) + p\)
\((20,\!000 - 500p) - p\)
\(\dfrac{20,000 - 500p}{p}\)
\((20,\!000 - 500p) \boldcdot p\)

Problem 7

ForLesson 9: Standard Form and Factored Form

Write each quadratic expression in standard form. Draw a diagram if needed.

\((x-3)(x-6)\)
\((x-4)^2\)
\((2x+3)(x-4)\)
\((4x-1)(3x-7)\)

Problem 8

ForLesson 9: Standard Form and Factored Form

Consider the expression \((5+x)(6-x)\).

Is the expression equivalent to \(x^2+x+30\)? Explain how you know.
Is the expression \(30+x+x^2\) in standard form? Explain how you know.