Explanation Given Information: The given quadratic equation is y = 12 x − 9 − 4 x 2 . …… (1) Formula used: The quadratic equation a x 2 + b x + c = 0 represents a parabola. If a is positive, then parabola opens upward. If a is negative, then parabola opens downward. The quadratic function is y = f ( x ) = a x 2 + b x + c . The vertex of the parabola is ( − b 2 a , f ( − b 2 a ) ) . If a < 0 , then the vertex point is maximum point. If a > 0 , then the vertex point is minimum point. Zero product property: The general form of quadratic equation is a x 2 + b x + c = 0 where a , b , c are constants and a ≠ 0 . For real numbers a and b , a b = 0 if and only if a = 0 or b = 0 or both . Calculation: To find the vertex, first check the value of a . a = − 4 < 0 The graph opens downward and the vertex is the maximum point. Compare the equation (1) with the quadratic function. a = − 4 and b = 12 Use the formula of the vertex ( − b 2 a , f ( − b 2 a ) ) . ( x , y ) = ( − b 2 a , f ( − b 2 a ) ) = ( − 12 2 ( − 4 ) , 12 ( − 12 2 ( − 4 ) ) − 9 − 4 ( − 12 2 ( − 4 ) ) 2 ) = ( 3 2 , 12 ( 3 2 ) − 9 − 4 ( 3 2 ) 2 ) = ( 3 2 , 18 − 9 − 9 ) = ( 1

Student Solutions Manual for Harshbarger/Reynolds's Mathematical Applications for the Management, Life, and Social Sciences, 12th

12th Edition

ISBN: 9781337630467

Author: Ronald J. Harshbarger; James J. Reynolds

Publisher: Cengage Learning

See similar textbooks

Concept explainers

Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.

Videos

Question

Chapter 2, Problem 24RE

To determine

To calculate: The vertex and determine if it is a maximum or minimum point of the quadratic equation y=12x−9−4x2. Also, find the y− intercept and the zeros and draw the graph.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 2, Problem 23RE

Chapter 2, Problem 25RE

Students have asked these similar questions

Pls help ASAP

2. Sam and Deb have a weekly net income of $1500. They have a pet dog. Their monthly expenses, not related to housing, are $2875. They have savings of $32 000. They are considering two housing options: Option 1: Renting a 2-bedroom condo for $1650 a month, plus utilities averaging $210 a month Option 2: Buying a 2-bedroom condo for a down payment of $24 500, bi-weekly mortgage payments of $1100, and a monthly condo fee of $475 a) Determine the monthly cost of each housing option. Factoring in other expenses not related to housing, which one can Sam and Deb afford? b) Suppose their dog falls ill and they have to pay $85 every week to cover veterinarian and medical expenses. Calculate the additional monthly expenses. How much money would be available for savings if they choose housing option 2?

I bought sparrows at 3 for a penny, turtle doves at 2 for a penny, anddoves at 2 pence each. If I spent 30 pence buying 30 birds and boughtat least one of each kind of bird, how many birds of each kind did I buy?(This is a problem from Fibonacci’s Liber Abaci, 1202.)

Chapter 2 Solutions

Student Solutions Manual for Harshbarger/Reynolds's Mathematical Applications for the Management, Life, and Social Sciences, 12th

Ch. 2.1 - The factoring method for solving a quadratic...Ch. 2.1 - Solve the following equations by factoring. Ch. 2.1 - Prob. 3CP Ch. 2.1 - Prob. 4CP Ch. 2.1 - Prob. 1E Ch. 2.1 - Prob. 2E Ch. 2.1 - Prob. 3E Ch. 2.1 - Prob. 4E Ch. 2.1 - In Problems 5-14, solve each question by...Ch. 2.1 - Prob. 6E

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

The vertex and determine if it is a maximum or minimum point of the quadratic equation y = 12 x − 9 − 4 x 2 . Also, find the y − intercept and the zeros and draw the graph.

Solution Summary: The author calculates the vertex and determines if it is a maximum or minimum point of the quadratic equation.

Concept explainers

Videos

To calculate: The vertex and determine if it is a maximum or minimum point of the quadratic equation y=12x−9−4x2. Also, find the y− intercept and the zeros and draw the graph.

Want to see the full answer?

Chapter 2 Solutions