(a) Explanation Definition used: “The equation of shifted parabola with vertex V ( h , k ) is ( x − h ) 2 = 4 p ( y − k ) ” “The equation of the parabola with vertex V ( 0 , 0 ) , focus F ( 0 , p ) and directrix y = − p is x 2 = 4 p y ”. “If h and k are any two positive real numbers and a graph of any equation is in terms of x and y then. ( i ) Replacing x by x − h , shift the graph right to h units. ( i i ) Replacing x by x + h , shift the graph left to h units. ( i i i ) Replacing y by y − k , shift the graph upward to k units. ( i v ) Replacing y by y + k , shift the graph downward to k units.” The given equation of conic is ( x + 3 ) 2 = − 20 ( y + 2 ) . Use the definition “The equation of shifted parabola with vertex V ( h , k ) is ( x − h ) 2 = 4 p ( y − k ) ” in the equation of parabola ( x + 3 ) 2 = − 20 ( y + 2 ) . Here, h = − 3 and k = − 2 . Therefore, by above definition the vertex of the parabola ( x + 3 ) 2 = − 20 ( y + 2 ) is V ( − 3 , − 2 ) . The equation ( x + 3 ) 2 = − 20 ( y + 2 ) is the shifted parabolic equation of x 2 = − 20 y . The equation of parabola x 2 = − 20 y may obtain as from the equation of parabola ( x + 3 ) 2 = − 20 ( y + 2 ) by replacing x by x + 3 and y by y + 2 . Therefore, the focus and directrix of the parabola ( x + 3 ) 2 = − 20 ( y + 2 ) may obtain as by shift the x-coordinates by 3 units left and y-coordinates by 2 units downward in the focus and directrix of the parabola x 2 = − 20 y (b) To determine To sketch: The graph and directrix of the parabola ( x + 3 ) 2 = − 20 ( y + 2 ) .

Bundle: Precalculus: Mathematics for Calculus, 7th + WebAssign Printed Access Card for Stewart/Redlin/Watson's Precalculus, Enhanced Edition, 7th Edition, Single-Term

7th Edition

ISBN: 9781305701618

Author: James Stewart, Lothar Redlin, Saleem Watson

Publisher: Cengage Learning

See similar textbooks

Concept explainers

Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.

Videos

Question

Chapter 11, Problem 8RE

(a)

To determine

To find: The vertex, focus and directrix of the parabola (x+3)2=−20(y+2) .

(b)

To determine

To sketch: The graph and directrix of the parabola (x+3)2=−20(y+2) .

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 11, Problem 7RE

Chapter 11, Problem 9RE

Students have asked these similar questions

Write an equation for the polynomial graphed below 5+ 4 3 1 + + + -5-4-3-2 1 13 4 5 -1 -2 -3 -4 -5+ 4 5 Q y(x) =

3. Solve the inequality, and give your answer in interval notation. - (x − 4)³ (x + 1) ≥ 0

1. Find the formula to the polynomial at right. Show all your work. (4 points) 1- 2 3 сл 5 6 -4 -3 -2 -1 0 2 3

Chapter 11 Solutions

Bundle: Precalculus: Mathematics for Calculus, 7th + WebAssign Printed Access Card for Stewart/Redlin/Watson's Precalculus, Enhanced Edition, 7th Edition, Single-Term

Ch. 11.1 - A parabola is the set of all points in the plane...Ch. 11.1 - The graph of the equation x2 = 4py is a parabola...Ch. 11.1 - The graph of the equation y2 = 4px is a parabola...Ch. 11.1 - Label the focus, directrix, and vertex on the...Ch. 11.1 - Graphs of Parabolas Match the equation with the...Ch. 11.1 - Prob. 6E Ch. 11.1 - Graphs of Parabolas Match the equation with the...Ch. 11.1 - Prob. 8E Ch. 11.1 - Graphs of Parabolas Match the equation with the...Ch. 11.1 - Graphs of Parabolas Match the equation with the...

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

The vertex, focus and directrix of the parabola ( x + 3 ) 2 = − 20 ( y + 2 ) .

Solution Summary: The author explains the vertex, focus, and directrix of the parabola.