(a) Explanation Formula used: Standard form: When the axis of symmetry is parallel to the y- axis, the standard form of the parabola is ( x − h ) 2 = 4 p ( y − k ) , where the vertex is ( h , k ) , the focus is ( h , k + p ) and the directrix is y = k − p . When the axis of symmetry is parallel to the y- axis, the standard form of the parabola is ( y − k ) 2 = 4 p ( x − h ) , where the vertex is ( h , k ) , the focus is ( h + p , k ) and the directrix is x = h − p . Vertical shift: If the variable y is changed by y ± a , then the graph of y shifts downward/upward by a units. Horizontal shift: If the variable x is changed by x ± b , then the graph of y shifts left/right by b units. Calculation: Compare the equation of the parabola x 2 = − 4 y with the standard form and obtain the value of h and k is 0. The value of p is given by, x 2 = 4 p y − 4 y = 4 p y p = − 1 Hence, the vertex of the parabola x 2 = − 4 y is ( 0 , 0 ) , the f (b) To determine To plot: The vertex, focus, and directrix of the new parabola and sketch the graph.

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ISBN: 9780134654874

Author: WEIR

Publisher: VST

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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.

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Chapter 11.6, Problem 40E

(a)

To determine

The vertex, focus, and directrix of the new parabola.

(b)

To determine

To plot: The vertex, focus, and directrix of the new parabola and sketch the graph.

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Chapter 11.6, Problem 39E

Chapter 11.6, Problem 41E

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