Unit 7, Lesson 12

Graphing the Standard Form (Part 1)

Algebra 1

Practice

Problem 1

Here are four graphs. Match each graph with a quadratic equation that it represents.

<p>A curve in an x y plane, origin O.</p> — Graph A

Graph A
Graph B
Graph C
Graph D

\(y = x^2\)
\(y = x^2 + 5\)
\(y = x^2 +7\)
\(y = x^2 - 3\)

Problem 2

The two equations \(y=(x+2)(x+3)\) and \(y=x^2 + 5x + 6\) are equivalent.

Which equation helps find the \(x\)-intercepts most efficiently?
Which equation helps find the \(y\)-intercept most efficiently?

Problem 3

Here is a graph that represents \(y = x^2\).

On the same coordinate plane, sketch and label the graph that represents each equation:

\(y = x^2 -4\)
\(y = \text-x^2 + 5\)

Problem 4

Select all equations whose graphs have a \(y\)-intercept with a positive \(y\)-coordinate.

\(y=x^2 + 3x - 2\)
\(y=x^2 - 10x\)
\(y=(x-1)^2\)
\(y=5x^2-3x-5\)
\(y=(x+1)(x+2)\)

Problem 5

ForLesson 14: Absolute Value Functions (Part 2)

Describe how the graph of \(A(x)=|x|\) has to be shifted to match the given graph.
Write an equation for the function represented by the graph.

<p>Absolute value function with vertex at 2 comma 3.</p>

Problem 6

ForLesson 13: Reasoning about Exponential Graphs (Part 2)

Here is a graph of a function, \(g\), given by \(g(x) = a \boldcdot b^x\).

What can you say about the value of \(b\)? Explain how you know.

<p>Graph of a decreasing exponential function g, x y plane, origin O.</p>

Problem 7

ForLesson 11: Graphing from the Factored Form

What are the \(x\)-intercepts of the graph that represents \(y = (x+1)(x+5)\)? Explain how you know.
What is the \(x\)-coordinate of the vertex of the graph that represents \(y = (x+1)(x+5)\)? Explain how you know.
Find the \(y\)-coordinate of the vertex. Show your reasoning.
Sketch a graph of \(y = (x+1)(x+5)\).

Problem 8

ForLesson 11: Graphing from the Factored Form

Determine the \(x\)-intercepts, the vertex, and the \(y\)-intercept of the graph of each equation.

equation	\(x\)-intercepts	vertex	\(y\)-intercept
\(y=(x-5)(x-3)\)
\(y=2x(8-x)\)

Problem 9

ForLesson 15: Functions Involving Percent Change

Equal amounts of money were invested in stock A and stock B. In the first year, stock A increased in value by 20%, and stock B decreased by 20%. In the second year, stock A decreased in value by 20%, and stock B increased by 20%.

Was one stock a better investment than the other? Explain your reasoning.

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