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 6²(c) Step 3: Go back to Step 1, and look at that part of that does not depend uponx. Call it K = +. Show that K can be positive or negative depending uponthe values of the parameters (a, b, c). Show that the effect of K is to shift (x+2)²up or down by a constant amount. Conclude that f(x)2a(x + 2)² - ² + isa2a=simply the function 2² shifted horizontally so it sits at x =2aand then it is shifted up or down by the amount K: upwards when K > 0 anddownwards when K <0. See hint in Step 4.on the x-axis

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Answered: start with quadratic function is f(x)=…

Math

Advanced Math

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

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.3: The Natural Exponential Function

Problem 4E

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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

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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