Unit 4, Lesson 12

Graphing the Standard Form (Part 1)

$Course Icon$

Integrated Math 2

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

$y = x^2$
$y = x^2 + 5$
$y = x^2 +7$
$y = x^2 - 3$

to access Practice Problem Solutions.

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?

to access Practice Problem Solutions.

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:

$y = x^2 -4$
$y = \text-x^2 + 5$

to access Practice Problem Solutions.

Problem 4

Select all equations whose graphs have a $y$-intercept with a positive $y$-coordinate.

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

to access Practice Problem Solutions.

Problem 5

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 $y = (x+1)(x+5)$.

to access Practice Problem Solutions.

Problem 6

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
$y=(x-5)(x-3)$
$y=2x(8-x)$

to access Practice Problem Solutions.

Problem 7

ForLesson 13: Weighted Averages in a Triangle

Triangle $ABC$ has vertices at $(0,0), (5,5),$ and $(10,1)$. Kiran calculates the point of intersection of the medians using the following steps:

Draw the triangle.
Calculate the midpoint of each side.
Draw the medians.
Write an equation for 2 of the medians.
Solve the system of equations.

Use Kiran’s method to calculate the point of intersection of the medians.

to access Practice Problem Solutions.

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

Navigation

Gradeband

Course

Unit

Lesson

Settings

Audience

Assessment Access

Lesson | Practice | Loading...

Settings

Audience

Assessment Access

Graphing the Standard Form (Part 1)

Practice

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Lesson 12 Resources