Skip to main content
Ch. 2 - Functions and Graphs
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook
All textbooksBlitzer 8th EditionCh. 2 - Functions and GraphsProblem 105
Chapter 3, Problem 105

Exercises 103–105 will help you prepare for the material covered in the next section. Solve by completing the square: y² – 6y — 4 = 0.

Verified step by step guidance
1
Start with the given quadratic equation: \(y^2 - 6y - 4 = 0\).
Move the constant term to the right side to isolate the terms involving \(y\): \(y^2 - 6y = 4\).
To complete the square, take half of the coefficient of \(y\) (which is \(-6\)), divide by 2 to get \(-3\), then square it to get \((-3)^2 = 9\).
Add 9 to both sides of the equation to maintain equality: \(y^2 - 6y + 9 = 4 + 9\).
Rewrite the left side as a perfect square trinomial: \((y - 3)^2 = 13\).

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
2m
Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Completing the Square

Completing the square is a method used to solve quadratic equations by transforming the equation into a perfect square trinomial. This involves adding and subtracting a specific value to create a binomial squared, making it easier to solve for the variable.
Recommended video:
06:24
Solving Quadratic Equations by Completing the Square

Quadratic Equations

A quadratic equation is a second-degree polynomial equation in the form ax² + bx + c = 0. Understanding its structure is essential for applying methods like completing the square, factoring, or using the quadratic formula to find the roots.
Recommended video:
05:35
Introduction to Quadratic Equations

Isolating the Variable

Isolating the variable means rearranging the equation so that the variable term stands alone on one side. This step is crucial before completing the square, as it simplifies the process and helps in accurately solving the equation.
Recommended video:
Guided course
05:28
Equations with Two Variables
Related Practice
Textbook Question

Begin by graphing the cube root function, f(x) = ∛x. Then use transformations of this graph to graph the given function. g(x) = ∛x+2

1142
views
Textbook Question

Begin by graphing the standard cubic function, f(x) = x³. Then use transformations of this graph to graph the given function. r(x) = (x − 2)³ +1

714
views
Textbook Question

In Exercises 107–108, write the standard form of the equation of the circle with the given center and radius. Center (-2. 4), r = 6

925
views
Textbook Question

Begin by graphing the standard cubic function, f(x) = x³. Then use transformations of this graph to graph the given function. h(x) = (1/2)(x − 2)³ – 1

829
views
Textbook Question

In Exercises 105–106, find the midpoint of each line segment with the given endpoints. (2, 6) and (-12, 4)

993
views
Textbook Question

Exercises 103–105 will help you prepare for the material covered in the next section. Use a rectangular coordinate system to graph the circle with center (1, -1) and radius 1.

817
views