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
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.7: Operations On Functions
Problem 2E
Related questions
Question
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa04b34b1-4a23-4a37-9f6a-b378054ef557%2F8ea23575-8173-4705-a2cb-40c4b03975db%2Fyv8fh0t_processed.png&w=3840&q=75)
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa04b34b1-4a23-4a37-9f6a-b378054ef557%2F8ea23575-8173-4705-a2cb-40c4b03975db%2Fxas23t_processed.png&w=3840&q=75)
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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