Homework Help is Here – Start Your Trial Now!
Math
Calculus
2.5 Quadratic Functions A quadratic function is given. a. Express the quadratic function in standard form. b. Find its vertex and its x- and y-intercept(s). c. Sketch its graph. d. Find its maximum or minimum value. f(x)= x - 2x + 2 a. Express the quadratic function in standard form. Group x and x erms. Add a blank to those terms and subtract a blank from the other S(x)= (x² - 2x+ D+2- terms. S(x) = (r* - 2x+1)+2-1 Fill in the blanks with Factor the grouped terms. It will always be f(x)= (x-1) +1 b. Find its vertex and its x- and y-intercept(s). y-intercept (let x=0 and solve): S(0) = 0² – 2(0)+2= 2 x-intercept (let y or f(x) =0 and solve): 0 = x' - 2x +2 Can't factor. %3D -b±vb -4ac -(-2)± (-2)° – 4(1)(2) 2a 2(1) 2+4-8 2+v-4 = non - real answer 2 (0, 2) is the y-intercept. There are no x-intercepts. c. Sketch its graph. d. Find its maximum or minimum value. Since the parabola opens up, there is a minimum point at the vertex. With the equation S(x)= (x-1)* +1 we know the vertex is (1, 1). Therefore, the minimum value is 1 and Ax) -2 -1 1 3 occurs when x=1. 4

2.5 Quadratic Functions A quadratic function is given. a. Express the quadratic function in standard form. b. Find its vertex and its x- and y-intercept(s). c. Sketch its graph. d. Find its maximum or minimum value. f(x)= x - 2x + 2 a. Express the quadratic function in standard form. Group x and x erms. Add a blank to those terms and subtract a blank from the other S(x)= (x² - 2x+ D+2- terms. S(x) = (r* - 2x+1)+2-1 Fill in the blanks with Factor the grouped terms. It will always be f(x)= (x-1) +1 b. Find its vertex and its x- and y-intercept(s). y-intercept (let x=0 and solve): S(0) = 0² – 2(0)+2= 2 x-intercept (let y or f(x) =0 and solve): 0 = x' - 2x +2 Can't factor. %3D -b±vb -4ac -(-2)± (-2)° – 4(1)(2) 2a 2(1) 2+4-8 2+v-4 = non - real answer 2 (0, 2) is the y-intercept. There are no x-intercepts. c. Sketch its graph. d. Find its maximum or minimum value. Since the parabola opens up, there is a minimum point at the vertex. With the equation S(x)= (x-1)* +1 we know the vertex is (1, 1). Therefore, the minimum value is 1 and Ax) -2 -1 1 3 occurs when x=1. 4

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
See similar textbooks
icon
Related questions
Question
2.5 Quadratic Functions A quadratic function is given. a. Express the quadratic function in standard form. b. Find its vertex and its x- and y-intercept(s). c. Sketch its graph. d. Find its maximum or minimum value. f(x)=x² - 2x+2 a. Express the quadratic function in standard form. Group x and x lerms. Add a blank to those terms and subtract a blank from the other S(x) = (x* – 2x + )+2- terms. S(x) = (r* - 2x+1)+2-1 Fill in the blanks with Factor the grouped terms. It will always be S(x) = (x – 1)* +1 x+ b. Find its vertex and its x- and y-intercept(s). y-intercept (let x=0 and solve): f(0) = 0² – 2(0)+ 2 = 2 x-intercept (let y or f(x) = 0 and solve): 0 = x' - 2x+2 Can't factor. -b±vb -4ac -(-2)± \(-2)° -4(1)(2) 2a 2(1) 2+4-8 x%3= 2+-4 = non - real answer %3D (0, 2) is the y-intercept. There are no x-intercepts. c. Sketch its graph. d. Find its maximum or minimum value. Since the parabola opens up, there is a minimum point at the vertex. Ax) L2 -1 With the equation f(x)=(x-1)* +1 we know the vertex is (1, 1). Therefore, the minimum value is 1 and occurs when x= 1. 4 étv N ост 14 MacBook Pro
Transcribed Image Text:2.5 Quadratic Functions A quadratic function is given. a. Express the quadratic function in standard form. b. Find its vertex and its x- and y-intercept(s). c. Sketch its graph. d. Find its maximum or minimum value. f(x)=x² - 2x+2 a. Express the quadratic function in standard form. Group x and x lerms. Add a blank to those terms and subtract a blank from the other S(x) = (x* – 2x + )+2- terms. S(x) = (r* - 2x+1)+2-1 Fill in the blanks with Factor the grouped terms. It will always be S(x) = (x – 1)* +1 x+ b. Find its vertex and its x- and y-intercept(s). y-intercept (let x=0 and solve): f(0) = 0² – 2(0)+ 2 = 2 x-intercept (let y or f(x) = 0 and solve): 0 = x' - 2x+2 Can't factor. -b±vb -4ac -(-2)± \(-2)° -4(1)(2) 2a 2(1) 2+4-8 x%3= 2+-4 = non - real answer %3D (0, 2) is the y-intercept. There are no x-intercepts. c. Sketch its graph. d. Find its maximum or minimum value. Since the parabola opens up, there is a minimum point at the vertex. Ax) L2 -1 With the equation f(x)=(x-1)* +1 we know the vertex is (1, 1). Therefore, the minimum value is 1 and occurs when x= 1. 4 étv N ост 14 MacBook Pro
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS