Explanation Consider the first set of parametric equations. x = ( t + 1 ) 2 …… (1) y = t + 2 …… (2) Simplify the equation (2) to get, t = y − 2 Substitute this value in equation (1) to get, x = ( y − 2 + 1 ) 2 = ( y − 1 ) 2 Thus, x = ( y − 1 ) 2 Now, consider the second set of parametric equation, x = ( t ) 2 …… (3) y = t + 1 …… (4) Simplify the second (4) to get, t = y − 1 Substitute this value in equation (3) to get, x = ( y − 1 ) 2 Both the sets of parametric equations have the same rectangular equation. Therefore, it can be said that they would have the same graph. Now, make the graph for the parametric equation with the help of a Ti-83 calculator. Step 1: Press ON key. Step 2: Press MODE key, choose the parametric option and press ENTER key. Step 3: Press Y= key and write the function as X 1T = ( T + 1 ) 2 Y 1T = T + 2 Step 4: Press WINDOW key to set the window setting. Tmin = − 10 , Tmax = 10,Tstep = 0 .5; X min = − 2 ; X max = 10 ; X scl = 2 Y min = − 2 ; Y max = 4 ; Y scl = 2 Step 5: Press GRAPH key

Bundle: Trigonometry, 10th + Webassign Printed Access Card For Larson's Trigonometry, 10th Edition, Single-term

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ISBN: 9781337605175

Author: Ron Larson

Publisher: Cengage Learning

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Chapter 6.6, Problem 110E

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Whether the graph for the parametric equations x=(t+1)2 and y=t+2 change or remains the same as the graph for the parametric equations x=(t)2 and y=t+1 as shown below.

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Chapter 6.6, Problem 109E

Chapter 6.7, Problem 1ECP

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Bundle: Trigonometry, 10th + Webassign Printed Access Card For Larson's Trigonometry, 10th Edition, Single-term

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Whether the graph for the parametric equations x = ( t + 1 ) 2 and y = t + 2 change or remains the same as the graph for the parametric equations x = ( t ) 2 and y = t + 1 as shown below.

Solution Summary: The author explains that the graph for the parametric equations x=(t+1)2 and y=t+2 would not change and remains the same.

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Whether the graph for the parametric equations x=(t+1)2 and y=t+2 change or remains the same as the graph for the parametric equations x=(t)2 and y=t+1 as shown below.

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