MATH SOLVE

5 months ago

Q:
# Match each function formula with the corresponding transformation of the parent function y = (x - 1)2 1.y = - (x - 1)2Translated right by 1 unit2.y = (x - 1)2 + 1Reflected over the y-axis3.y = (x + 1)2Translated left by 4 units4.y = (x - 2)2Translated up by 1 unit5.y = (x - 1)2 - 3 Translated down by 3 units6.y = (x + 3)2Reflected over the x-axis

Accepted Solution

A:

Answer:Always remember general rules of transformation.1) Vertical Shift: y= f(x)+k ; shifts the graph of f up k units if k>0, shifts it down |k| units if k<0.2) Horizontal Shift:y=f(x+h) ; shifts the graph of f left h units if h>0, shifts it right |h| units if h<0.3) Reflection across x-axisy= - f(x) ; reflect the graph of f across the x-axis.Now,The parent function is y= -(x+2)²1. y= -(x+4)²In this question +2 is added with x+2 and becomes y= -(x+2+2)²=-(x+4)²So, according to rule 2 it will shift the parent function to the left by 2 units.E is the correct option.2. y = - (x + 2)² - 2 In this question, -2 is added to the parent function and we get y= - (x + 2)² - 2 So, according to rule 1, it will shift the graph down by 2 units.F is the correct option.3. y=(x - 2)² In this question, two operations are performed on the parent function.First one, -4 is added with x+2 so we get x+2-4= x-2Second one, -1 is multiplied with parent function.By performing the two operations at a time we get a new function which is y=-(-(x+2-4)²)=(x-2)²The first operation will translate the parent function 4 units right (according to rule 2).The second operation will reflect the graph across x-axis(according to rule 3).D and translation 4 units to right is correct option.4. y= 2 -(x+2)²In this question, we add +2 to the parent function so according to rule 1 it will shift the graph up by 2 units.C is the correct option.5. y= -x² In this question, we add -2 to x+2 so we get a new function y= -(x+2-2)²=-x²So, according to rule 2 it will shift the graph right by 2 units.B is the correct option.6. y= (x+2)²In this question, -1 is multiplied with parent function and we get y= -(-(x+2)²)= (x+2)²So, according to rule 3 , graph is reflected across x-axis. D is the correct answer.The graph of parent function and question no. 1,2,3 are attached separately, while question no. 4,5,6 are attached in combined form(due to space limit).Read more on Brainly.com - explanation: