![Algebra 1, Homework Practice Workbook (MERRILL ALGEBRA 1)](https://www.bartleby.com/isbn_cover_images/9780076602919/9780076602919_largeCoverImage.gif)
Concept explainers
a.
To graph the given function.
a.
![Check Mark](/static/check-mark.png)
Explanation of Solution
Given information :
Given function is
Graph :
Interpretation :
The graph of a
This vertex point shall be:
Highest point (if
Or, lowest point (if
In this case, ‘a’ is more than 0 hence the graph will have a minimum and will open upwards.
A parabola always points to infinity, either negative or positive.
To graph a quadratic function, compute the axis of symmetry, vertex and y-intercept, post which, plot the same on a graph.
The axis of symmetry bisects the parabola into two equal parts. Hence each point on the parabola would have an equal point on the other side of the axis of symmetry. Plot these points on the graph with a smooth curve.
Formula to compute equation of the axis of symmetry
Axis of symmetry for the given function is
Formula for axis of symmetry.
Putting the values of ‘a’ and ‘b’ .
Simplifying this
Vertex can be found out by putting the value of x computed in the axis of symmetry in the original function. This will give a value of y . These two coordinates of x and y would be the point where the vertex is.
Putting the value of
Simplifying the expression.
Thus the vertex is
y-intercept is computed by substituting the value of x in the equation by 0.
Simplifying
Hence the point of y-intercept is
Now, plot these points along with their reflecting symmetric points, starting from the vertex.
b.
To name the zeros of the function.
b.
![Check Mark](/static/check-mark.png)
Answer to Problem 38PPS
The zeros of the function are
Explanation of Solution
Given information :
The function is
Using the graphing calculator, the graph for the given function is:
Zeros of the parabola are the places where the parabola intersects the x-axis.
This given graph, the zeros are at
c.
To calculate factors of the given function.
c.
![Check Mark](/static/check-mark.png)
Answer to Problem 38PPS
The factors are
Explanation of Solution
Given information :
The function provided is
Formula used :
Factoring method involves in factorizing the terms in order to arrive at values that, if multiplied with each other, would provide the original quadratic function.
Calculation :
The graph of the given equation is
Breaking the middle term that when multiplied, provides that values of
Arranging the common elements.
The factors are
d.
To equate each factor with zero and find the result.
d.
![Check Mark](/static/check-mark.png)
Answer to Problem 38PPS
The results of x after equating with zero are -1 and 3 .
Explanation of Solution
Given information :
The function provided is
The graph of the given equation is
The factors are
Equating the factors with zero.
This is one result.
Equating the other factor with zero.
This is the other result.
e.
To draw conclusion regarding the factors of a quadratic equation.
e.
![Check Mark](/static/check-mark.png)
Answer to Problem 38PPS
The factors of a quadratic equation, if simplified with zero, would give its roots.
Explanation of Solution
Given information :
The function provided is
There are two factors of a quadratic equation. These factors, if multiplied, would yield the main equation. Also, if they are equated with zero, they provide the roots of the same quadratic equation.
When graphed, these roots are also called the zeros. They are the points where the graph meets the x-axis.
Chapter 9 Solutions
Algebra 1, Homework Practice Workbook (MERRILL ALGEBRA 1)
Additional Math Textbook Solutions
Pre-Algebra Student Edition
Basic Business Statistics, Student Value Edition
College Algebra with Modeling & Visualization (5th Edition)
Algebra and Trigonometry (6th Edition)
- Asked this question and got a wrong answer previously: Third, show that v3 = (−√3, −3, 3)⊤ is an eigenvector of M3 . Also here find the correspondingeigenvalue λ3 . Just from looking at M3 and its components, can you say something about the remaining twoeigenvalues? If so, what would you say?arrow_forwardDetermine whether the inverse of f(x)=x^4+2 is a function. Then, find the inverse.arrow_forwardThe 173 acellus.com StudentFunctions inter ooks 24-25/08 R Mastery Connect ac ?ClassiD-952638111# Introduction - Surface Area of Composite Figures 3 cm 3 cm 8 cm 8 cm Find the surface area of the composite figure. 2 SA = [?] cm² 7 cm REMEMBER! Exclude areas where complex shapes touch. 7 cm 12 cm 10 cm might ©2003-2025 International Academy of Science. All Rights Reserved. Enterarrow_forward
- You are given a plane Π in R3 defined by two vectors, p1 and p2, and a subspace W in R3 spanned by twovectors, w1 and w2. Your task is to project the plane Π onto the subspace W.First, answer the question of what the projection matrix is that projects onto the subspace W and how toapply it to find the desired projection. Second, approach the task in a different way by using the Gram-Schmidtmethod to find an orthonormal basis for subspace W, before then using the resulting basis vectors for theprojection. Last, compare the results obtained from both methodsarrow_forwardPlane II is spanned by the vectors: - (2) · P² - (4) P1=2 P21 3 Subspace W is spanned by the vectors: 2 W1 - (9) · 1 W2 1 = (³)arrow_forwardshow that v3 = (−√3, −3, 3)⊤ is an eigenvector of M3 . Also here find the correspondingeigenvalue λ3 . Just from looking at M3 and its components, can you say something about the remaining twoeigenvalues? If so, what would you say? find v42 so that v4 = ( 2/5, v42, 1)⊤ is an eigenvector of M4 with corresp. eigenvalue λ4 = 45arrow_forward
- Chapter 4 Quiz 2 As always, show your work. 1) FindΘgivencscΘ=1.045. 2) Find Θ given sec Θ = 4.213. 3) Find Θ given cot Θ = 0.579. Solve the following three right triangles. B 21.0 34.6° ca 52.5 4)c 26° 5) A b 6) B 84.0 a 42° barrow_forwardQ1: A: Let M and N be two subspace of finite dimension linear space X, show that if M = N then dim M = dim N but the converse need not to be true. B: Let A and B two balanced subsets of a linear space X, show that whether An B and AUB are balanced sets or nor. Q2: Answer only two A:Let M be a subset of a linear space X, show that M is a hyperplane of X iff there exists ƒ€ X'/{0} and a € F such that M = (x = x/f&x) = x}. fe B:Show that every two norms on finite dimension linear space are equivalent C: Let f be a linear function from a normed space X in to a normed space Y, show that continuous at x, E X iff for any sequence (x) in X converge to Xo then the sequence (f(x)) converge to (f(x)) in Y. Q3: A:Let M be a closed subspace of a normed space X, constract a linear space X/M as normed space B: Let A be a finite dimension subspace of a Banach space X, show that A is closed. C: Show that every finite dimension normed space is Banach space.arrow_forward• Plane II is spanned by the vectors: P12 P2 = 1 • Subspace W is spanned by the vectors: W₁ = -- () · 2 1 W2 = 0arrow_forward
- Algebra and Trigonometry (6th Edition)AlgebraISBN:9780134463216Author:Robert F. BlitzerPublisher:PEARSONContemporary Abstract AlgebraAlgebraISBN:9781305657960Author:Joseph GallianPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
- Algebra And Trigonometry (11th Edition)AlgebraISBN:9780135163078Author:Michael SullivanPublisher:PEARSONIntroduction to Linear Algebra, Fifth EditionAlgebraISBN:9780980232776Author:Gilbert StrangPublisher:Wellesley-Cambridge PressCollege Algebra (Collegiate Math)AlgebraISBN:9780077836344Author:Julie Miller, Donna GerkenPublisher:McGraw-Hill Education
![Text book image](https://www.bartleby.com/isbn_cover_images/9780134463216/9780134463216_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9781305657960/9781305657960_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9781285463247/9781285463247_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9780135163078/9780135163078_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9780980232776/9780980232776_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9780077836344/9780077836344_smallCoverImage.gif)