#1 # Graphing $ y = ax^2 $**Objective:**Understand how the graph of $ y = ax^2 $ changes when the coefficient $ a $ increases or decreases, and whether $ a $ is positive or negative.**Instructions:**Graph each pair of functions on the set of axes provided.**Equations and Graphs:**1. $ y = x^2 $ $ y = -x^2 $ - These equations are to be graphed on the first set of axes. - The graph of $ y = x^2 $ is a parabola opening upwards. - The graph of $ y = -x^2 $ is a parabola opening downwards. 2. $ y = 2x^2 $ $ y = -2x^2 $ - These equations are to be graphed on the second set of axes. - The graph of $ y = 2x^2 $ is a parabola opening upwards, which is narrower than the graph of $ y = x^2 $. - The graph of $ y = -2x^2 $ is a parabola opening downwards, which is narrower than the graph of $ y = -x^2 $. 3. $ y = \frac{1}{2}x^2 $ $ y = 3x^2 $ - These equations are to be graphed on the third set of axes. - The graph of $ y = \frac{1}{2}x^2 $ is a parabola opening upwards, which is wider than the graph of $ y = x^2 $. - The graph of $ y = 3x^2 $ is a parabola opening upwards, which is narrower than the graph of $ y = x^2 $.**Graphical Explanation:**Each of the three provided sets of axes feature an x-y coordinate plane:- The x-axis and y-axis extend from -4 to 4 in both directions.- The first set of axes is intended for plotting $ y = x^2 $ and $ y = -x^2 $.- The second set of axes is for $ y = 2x^2 $ and $ y = -2x^2 $.- The third set of axes is for

Name: #1 # Graphing $ y = ax^2 $**Objective:**Understand how the graph of
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Description: #1 # Graphing $ y = ax^2 $**Objective:**Understand how the graph of $ y = ax^2 $ changes when the coefficient $ a $ increases or decreases, and whether $ a $ is positive or negative.**Instructions:**Graph each pair of functions on the set of

When we have function y =ax2 ,the graph will be upward parabola. When we have function y =-ax2 ,the…

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Graphing y = ax² %3D How does a graph of y = ax2 change when a, the coefficient of x2, increases or decreases or when a is positive or negative? Graph each pair of functions on the set of axes provided. 1. y = x2 2. y = 2x2 y = -x2 y = -2x2 y -2 2 -4 -2 2. -2

Graphing y = ax² %3D How does a graph of y = ax2 change when a, the coefficient of x2, increases or decreases or when a is positive or negative? Graph each pair of functions on the set of axes provided. 1. y = x2 2. y = 2x2 y = -x2 y = -2x2 y -2 2 -4 -2 2. -2

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Concept explainers

Addition Rule of Probability

It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.

Expected Value

When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).

Probability Distributions

Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.

Basic Probability

The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.

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Question

# Graphing $ y = ax^2 $

**Objective:**
Understand how the graph of $ y = ax^2 $ changes when the coefficient $ a $ increases or decreases, and whether $ a $ is positive or negative.

**Instructions:**
Graph each pair of functions on the set of axes provided.

**Equations and Graphs:**

1. $ y = x^2 $
$ y = -x^2 $

- These equations are to be graphed on the first set of axes.
- The graph of $ y = x^2 $ is a parabola opening upwards.
- The graph of $ y = -x^2 $ is a parabola opening downwards.

2. $ y = 2x^2 $
$ y = -2x^2 $

- These equations are to be graphed on the second set of axes.
- The graph of $ y = 2x^2 $ is a parabola opening upwards, which is narrower than the graph of $ y = x^2 $.
- The graph of $ y = -2x^2 $ is a parabola opening downwards, which is narrower than the graph of $ y = -x^2 $.

3. $ y = \frac{1}{2}x^2 $
$ y = 3x^2 $

- These equations are to be graphed on the third set of axes.
- The graph of $ y = \frac{1}{2}x^2 $ is a parabola opening upwards, which is wider than the graph of $ y = x^2 $.
- The graph of $ y = 3x^2 $ is a parabola opening upwards, which is narrower than the graph of $ y = x^2 $.

**Graphical Explanation:**

Each of the three provided sets of axes feature an x-y coordinate plane:

- The x-axis and y-axis extend from -4 to 4 in both directions.
- The first set of axes is intended for plotting $ y = x^2 $ and $ y = -x^2 $.
- The second set of axes is for $ y = 2x^2 $ and $ y = -2x^2 $.
- The third set of axes is for

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