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Chapter 11: Q. 11.36TI (page 1069)

(a) Write x=-4y2-16y-12in 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=-4(y+2)2+4

Part (b), The graph is

Step by step solution

01

Part (a) Step 1: Given information

Given functionx=-4y2-16y-12

02

Part (a) Step 2: Rewriting the function

Rewriting, we get

x=-4y2-16y-12x=-4(y2+4y)-12x=-4(y+2)2+4

03

Part (b) Step 1: Given information

Given the standard formx=-4(y+2)2+4

04

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

Calculating, we get

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

05

Part (b) Step 3: Calculate the x intercept

Calculating, we get

x=-4(y+2)2+4x=-4(0+2)2+4x=-12

06

Part (b) Step 4: Calculate the y intercept

Calculating, we get

x=-4(y+2)2+4-4(y+2)2+4=0-4(y+2)2=-4(y+2)2=1y=-1,-3

07

Part (b) Step 5: Sketching the graph

The graph is

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