To determine To find: The lists of the intercepts of the equation y = x 2 − 9 . Explanation Given: The equation y = x 2 − 9 . Formula used: 1. If the discriminant b 2 − 4 a c > 0 , the graph of f ( x ) = a x 2 + b x + c has two distinct x -intercepts so it crosses the x -axis in two places. 2. If the discriminant b 2 − 4 a c = 0 , the graph of f ( x ) = a x 2 + b x + c has only one x -intercept so it touches the x -axis at its vertex. 3. If the discriminant b 2 − 4 a c < 0 , the graph of f ( x ) = a x 2 + b x + c has no x -intercept so it does not cross or touch the x -axis . Calculation: Compare the equation y = x 2 − 9 from the general quadratic equation f ( x ) = a x 2 + b x + c , so it give a = 1 , b = 0 and c = − 9 . The discriminant b 2 − 4 a c is, b 2 − 4 a c = ( 0 ) 2 − 4 ⋅ 1 ⋅ ( − 9 ) = 0 + 36 = 36 Here observed that the discriminant b 2 − 4 a c > 0 ...

College Algebra Enhanced with Graphing Utilities (7th Edition) (Sullivan Enhanced with Graphing Utilities Series)

7th Edition

ISBN: 9780134111315

Author: Michael Sullivan, Michael Sullivan III

Publisher: PEARSON

See similar textbooks

Concept explainers

Family of Curves

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These…

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are…

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) ge…

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.

Videos

Question

Chapter 4.3, Problem 1AYU

To determine

To find: The lists of the intercepts of the equation $y = x^{2} - 9$ .

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4.2, Problem 31AYU

Chapter 4.3, Problem 2AYU

Students have asked these similar questions

Solve the system of equation for y using Cramer's rule. Hint: The determinant of the coefficient matrix is -23. - 5x + y − z = −7 2x-y-2z = 6 3x+2z-7

eric pez Xte in z= Therefore, we have (x, y, z)=(3.0000, 83.6.1 Exercise Gauss-Seidel iteration with Start with (x, y, z) = (0, 0, 0). Use the convergent Jacobi i Tol=10 to solve the following systems: 1. 5x-y+z = 10 2x-8y-z=11 -x+y+4z=3 iteration (x Assi 2 Assi 3. 4. x-5y-z=-8 4x-y- z=13 2x - y-6z=-2 4x y + z = 7 4x-8y + z = -21 -2x+ y +5z = 15 4x + y - z=13 2x - y-6z=-2 x-5y- z=-8 realme Shot on realme C30 2025.01.31 22:35 f

Use Pascal's triangle to expand the binomial (6m+2)^2

Chapter 4 Solutions

College Algebra Enhanced with Graphing Utilities (7th Edition) (Sullivan Enhanced with Graphing Utilities Series)

Ch. 4.1 - Answers are given at the end of these exercises....Ch. 4.1 - Prob. 2AYU Ch. 4.1 - Prob. 3AYU Ch. 4.1 - Prob. 4AYU Ch. 4.1 - Prob. 5AYU Ch. 4.1 - Prob. 6AYU Ch. 4.1 - Prob. 7AYU Ch. 4.1 - Prob. 8AYU Ch. 4.1 - 9. True or False The slope of a nonvertical line...Ch. 4.1 - Prob. 10AYU

Knowledge Booster

$Algebra$

Learn more about

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