/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 23 Find the quadratic function \(y=... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 23

Find the quadratic function \(y=a x^{2}+b x+c\) whose graph passes through the given points. $$(-1,-4),(1,-2),(2,5)$$

Short Answer

Expert verified
The quadratic function that passes through the points (-1,-4), (1,-2), (2,5) is \(y=x^2+x-4\).

Step by step solution

01

Set up equations

From the three given points (-1,-4), (1,-2), (2,5), we formulate three equations by substituting the x and y values into the quadratic function, resulting in: \[ -4=a(-1)^2+b(-1)+c \] \[ -2=a(1)^2+b(1)+c \] \[ 5=a(2)^2+b(2)+c \]which can be rewritten as \[-4=a-b+c\] \[-2=a+b+c\] \[5=4a+2b+c.\]
02

Solve the system of equations

We can solve this system of equations using the method of substitution or elimination. Start by subtracting the second equation from the first to get \[-2=-2b\], or \(b=1\). Substituting \(b=1\) into the first and second equations, we get \(a+c=-3\) and \(a+c=-1\). Solving these results give us \(c=-4\) and \(a=1\).
03

Validate the solution

Substitute \(a=1\), \(b=1\), \(c=-4\) into the third equation and confirm if the equation holds true. This results in: \(5=4(1)+2*1-4 = 5\), confirming our solutions are accurate.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

In Exercises \(19-30,\) solve each system by the addition method. \(3 x=4 y+1\) \(3 y=1-4 x\)

Exercises \(47-50\) describe a number of business ventures. For each exercise, a. Write the cost function, \(C\). b. Write the revenue function, \(R\) c. Determine the break-even point. Describe what this means. You invest in a new play. The cost includes an overhead of \(\$ 30,000,\) plus production costs of \(\$ 2500\) per performance. A sold-out performance brings in \(\$ 3125\). (In solving this exercise, let \(x\) represent the number of sold-out performances.)

In Exercises \(5-18\), solve each system by the substitution method. $$ \begin{aligned} &2 x-3 y=-13\\\ &y=2 x+7 \end{aligned} $$

In Exercises \(31-42,\) solve by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. \(3 x-2 y=-5\) \(4 x+y=8\)In Exercises \(31-42,\) solve by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. \(3 x-2 y=-5\) \(4 x+y=8\)

In Exercises \(5-18\), solve each system by the substitution method. $$ \begin{aligned} &y=\frac{1}{3} x+\frac{2}{3}\\\ &y=\frac{5}{7} x-2 \end{aligned} $$
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Mechanics Maths

Read Explanation

Logic and Functions

Read Explanation

Geometry

Read Explanation

Statistics

Read Explanation

Applied Mathematics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.