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1. Work with the quadratic function y(x) = 2x² + 2x + 2. (a) Find the roots. (b) Define the axis of symmetry and calculate its value. (c) Does the function have a maximum or a minimum? Why? (d) What is the value of the function at the maximum (or minimum)? (e) Graph the function.

1. Work with the quadratic function y(x) = 2x² + 2x + 2. (a) Find the roots. (b) Define the axis of symmetry and calculate its value. (c) Does the function have a maximum or a minimum? Why? (d) What is the value of the function at the maximum (or minimum)? (e) Graph the function.

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...
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1. Work with the quadratic function y(x) = 2x² + 2x + 2. (a) Find the roots. (b) Define the axis of symmetry and calculate its value. (c) Does the function have a maximum or a minimum? Why? (d) What is the value of the function at the maximum (or minimum)? (e) Graph the function. 0 @ 1 = - 12/2 2. -√√-3 r₂ = -2 +15=3 2 2 (D (b) The axis of symmetry is the line about which y(x) is symmetric. x* = 1₁+√₂ = 1/2 Ⓒ (c) The function has a minimum at x =-½/2 because aso y (-2) = ²/3 - ²/2 +2 2 Ⓒ (d) (e) - ½/22 1 दू In yo O VIT = 6 x
Transcribed Image Text:1. Work with the quadratic function y(x) = 2x² + 2x + 2. (a) Find the roots. (b) Define the axis of symmetry and calculate its value. (c) Does the function have a maximum or a minimum? Why? (d) What is the value of the function at the maximum (or minimum)? (e) Graph the function. 0 @ 1 = - 12/2 2. -√√-3 r₂ = -2 +15=3 2 2 (D (b) The axis of symmetry is the line about which y(x) is symmetric. x* = 1₁+√₂ = 1/2 Ⓒ (c) The function has a minimum at x =-½/2 because aso y (-2) = ²/3 - ²/2 +2 2 Ⓒ (d) (e) - ½/22 1 दू In yo O VIT = 6 x
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where did you get the 1/4's from in the highlighted part?

So given ac y y y = 2x² +2x+2 So at (1 = = 2 (x² + x) + 2 2 X (8 + 3) = 2) 2(x²+x+/4/4/4 - 4 - 4) 2 y = 2 ( x + 1)² - 3/2 funtion 2 ( x + ¹)² = ² ( + ₁) + - This parabola ²(x + 2) ² 2 is a has +2. upw and +2 minimum parabola.
Transcribed Image Text:So given ac y y y = 2x² +2x+2 So at (1 = = 2 (x² + x) + 2 2 X (8 + 3) = 2) 2(x²+x+/4/4/4 - 4 - 4) 2 y = 2 ( x + 1)² - 3/2 funtion 2 ( x + ¹)² = ² ( + ₁) + - This parabola ²(x + 2) ² 2 is a has +2. upw and +2 minimum parabola.
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