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start with quadratic function is f(x)= ax^2 + bx + c and follow the images questions

start with quadratic function is f(x)= ax^2 + bx + c and follow the images questions

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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start with quadratic function is f(x)= ax^2 + bx + c and follow the images questions

f(₂)=(x + 2)² +5 (a) Step 1: Show that f(¹) a
Transcribed Image Text:f(₂)=(x + 2)² +5 (a) Step 1: Show that f(¹) a
6² (c) Step 3: Go back to Step 1, and look at that part of that does not depend upon x. Call it K = +. Show that K can be positive or negative depending upon the values of the parameters (a, b, c). Show that the effect of K is to shift (x+2)² up or down by a constant amount. Conclude that f(x) 2a (x + 2)² - ² + is a 2 a = simply the function 2² shifted horizontally so it sits at x = 2a and then it is shifted up or down by the amount K: upwards when K > 0 and downwards when K <0. See hint in Step 4. on the x-axis
Transcribed Image Text:6² (c) Step 3: Go back to Step 1, and look at that part of that does not depend upon x. Call it K = +. Show that K can be positive or negative depending upon the values of the parameters (a, b, c). Show that the effect of K is to shift (x+2)² up or down by a constant amount. Conclude that f(x) 2a (x + 2)² - ² + is a 2 a = simply the function 2² shifted horizontally so it sits at x = 2a and then it is shifted up or down by the amount K: upwards when K > 0 and downwards when K <0. See hint in Step 4. on the x-axis
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