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Chapter 11: Q. 11.35TI (page 1098)

(a) Write x=3y2+6y+7in standard form and (b) use properties of the standard form to graph the equation.

Short Answer

Expert verified

Part (a), The standard form is x=3(y+1)2+4

Part (b), The graph is

Step by step solution

01

Part (a) Step 1: Given information

Given the functionx=3y2+6y+7

02

Part (a) Step 2: Rewriting the function

Rewriting, we get

x=3y2+6y+7x=3(y2+2y)+7x=3(y2+2y+12)+4x=3(y+1)2+4

03

Part (b) Step 1: Given information

Given the standard formx=3(y+1)2+4

04

Part (b) Step 2: Identify the constants a, h, k and the other parameters

Comparing, we get

x=3(y+1)2+4a=3(h,k)=(4,-1)

05

Part (b) Step 3: Calculate x intercept

Calculating, we get

x=3(y+1)2+4x=3(0+1)2+4x=7

06

Part (b) Step 4: Calculating y intercept

Calculating, we get

x=3(y+1)2+43(y+1)2+4=03(y+1)2=-4

Square can't be negative so there is noyintercept

07

Part (b) Step 5: Sketching the graph

The graph is

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