/*! 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 241 Find the intercepts of the parab... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 9: Problem 241

Find the intercepts of the parabola whose function is given. $$f(x)=x^{2}+7 x+6$$

Short Answer

Expert verified
The y-intercept is 6. The x-intercepts are -1 and -6.

Step by step solution

01

Identify the y-intercept

To find the y-intercept, substitute 0 for x in the function. Given function: Replace x with 0: . Thus, y-intercept: .
02

Equation to find y-intercept

To find the y-intercept, f(0) = 0^2 + 7*0 + 6. The y-intercept is 6
03

Identify the x-intercepts

To find the x-intercepts, set the function equal to 0 and solve for x: . The solutions to this quadratic equation will be the x-intercepts.
04

Solve the quadratic equation

Use factoring to solve the equation . Find two numbers that multiply to 6 and add to 7. The factors of the quadratic equation are: . Set each factor equal to 0: and . The x-intercepts are and .

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!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Quadratic Function
A quadratic function is a type of polynomial function where the highest degree of the variable is 2. It is generally written in the form: The graph of a quadratic function is a parabola, which can either open upwards or downwards. In our example, the quadratic function is given as: In this case, by analyzing the coefficients, you can observe that the parabola opens upwards because the coefficient of the term is positive.
Y-Intercept
The y-intercept of a function is the point where the graph of the function crosses the y-axis. To find the y-intercept, we simply substitute 0 for x in the function because any point on the y-axis has an x-coordinate of 0. For example, if we have the function: To find the y-intercept, set x to 0: This simplifies to: Therefore, the y-intercept of the parabola described by the function is 6. In coordinate form, it is written as (0, 6).
X-Intercepts
The x-intercepts are the points where the parabola crosses the x-axis. These are found by setting the quadratic function equal to zero and solving for x because any point on the x-axis has a y-coordinate of 0. For the function we need to solve this equation: To solve for the x-intercepts, we can use factoring. We factorize the quadratic expression to find values of x that satisfy the equation.
Factoring
Factoring is a method used to solve quadratic equations by expressing the quadratic expression as a product of its linear factors. For our function we need to determine two numbers that multiply to the constant term (6) and add up to the coefficient of the linear term (7). The two numbers that meet these criteria are 1 and 6, because: 1*6 = 6 and 1+6 = 7 Using these numbers, we can factor the function as: Setting each factor equal to zero provides the solutions: and Therefore, the x-intercepts are -1 and -6, or in coordinate form: (-1, 0) and (-6, 0).

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

Solve each inequality algebraically and write any solution in interval notation. $$x^{2}-4 x+2 \leq 0$$

Find the intercepts of the parabola whose function is given. $$f(x)=x^{2}+6 x+13$$

Solve. Round answers to the nearest tenth. A ball is thrown vertically upward from the ground with an initial velocity of \(122 \mathrm{ft} / \mathrm{sec}\). Use the quadratic function \(h(t)=-16 t^{2}+122 t+0\) to find how long it will take for the ball to reach its maximum height, and then find the maximum height.

(a) solve graphically and (b) write the solution in interval notation. $$x^{2}+6 x+5>0$$

Find the maximum or minimum value of each function. $$y=4 x^{2}-49$$
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Logic and Functions

Read Explanation

Decision Maths

Read Explanation

Mechanics Maths

Read Explanation

Statistics

Read Explanation

Theoretical and Mathematical Physics

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.