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Chapter 10: Q 14. (page 643)

The graph of a parabola is given. Match graph to its equation.

and equations of the parabola areA)y2=4xC)y2=-4xE)(y-1)2=4(x-1)G)(y-1)2=-4(x-1)B)x2=4yD)x2=-4yF)(x+1)2=4(y+1)H)(x+1)2=4(y+1)

Short Answer

Expert verified

The correct match is (D).

Step by step solution

01

Step 1. Given information.

We have given graph is,

And given equations of the parabola isA)y2=4xC)y2=-4xE)(y-1)2=4(x-1)G)(y-1)2=-4(x-1)B)x2=4yD)x2=-4yF)(x+1)2=4(y+1)H)(x+1)2=4(y+1)

02

Step 2. Concept used.

General equation of the parabola is,x-h2=4ay-k鈥�and鈥�y-k2=4ax-h

03

Step 3. Explanation.

We have given graph is,

This graph is opens down and vertex of the graph is (0, 0) and point on the graph is

(-2, -1).

Using standard equation of the parabola,

(x-h)2=4a(y-k)鈬�(x-0)2=4a(y-0)鈬�x2=4ay

Using the point, (-2, -1)

localid="1646817023642" 4=-4a鈬�a=-1鈬�x2=-4y

04

Step 4. Conclusion.

Hence, equation of the graph

isx2=-4y

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