Chapter 10: Q 14. (page 643)

The graph of a parabola is given. Match graph to its equation.
and equations of the parabola are $A) y^{2} = 4 x C) y^{2} = - 4 x E) {(y - 1)}^{2} = 4 (x - 1) G) {(y - 1)}^{2} = - 4 (x - 1) B) x^{2} = 4 y D) x^{2} = - 4 y F) {(x + 1)}^{2} = 4 (y + 1) H) {(x + 1)}^{2} = 4 (y + 1)$

Short Answer

Expert verified

The correct match is (D).

Step by step solution

Step 1. Given information.

We have given graph is,

And given equations of the parabola is $A) y^{2} = 4 x C) y^{2} = - 4 x E) {(y - 1)}^{2} = 4 (x - 1) G) {(y - 1)}^{2} = - 4 (x - 1) B) x^{2} = 4 y D) x^{2} = - 4 y F) {(x + 1)}^{2} = 4 (y + 1) H) {(x + 1)}^{2} = 4 (y + 1)$

Step 2. Concept used.

General equation of the parabola is, ${(x - h)}^{2} = 4 a (y - k) a n d {(y - k)}^{2} = 4 a (x - h)$

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,

${(x - h)}^{2} = 4 a (y - k) \Rightarrow {(x - 0)}^{2} = 4 a (y - 0) \Rightarrow x^{2} = 4 a y$

Using the point, (-2, -1)

localid="1646817023642" $4 = - 4 a \Rightarrow a = - 1 \Rightarrow x^{2} = - 4 y$

Step 4. Conclusion.

Hence, equation of the graph

is $x^{2} = - 4 y$

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The graph of a parabola is given. Match graph to its equation.
and equations of the parabola are $A) y^{2} = 4 x C) y^{2} = - 4 x E) {(y - 1)}^{2} = 4 (x - 1) G) {(y - 1)}^{2} = - 4 (x - 1) B) x^{2} = 4 y D) x^{2} = - 4 y F) {(x + 1)}^{2} = 4 (y + 1) H) {(x + 1)}^{2} = 4 (y + 1)$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Concept used.

Step 3. Explanation.

Step 4. Conclusion.

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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

Step by step solution

Step 1. Given information.

Step 2. Concept used.

Step 3. Explanation.

Step 4. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

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Applied Mathematics

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Study anywhere. Anytime. Across all devices.

The graph of a parabola is given. Match graph to its equation.
and equations of the parabola are $A) y^{2} = 4 x C) y^{2} = - 4 x E) {(y - 1)}^{2} = 4 (x - 1) G) {(y - 1)}^{2} = - 4 (x - 1) B) x^{2} = 4 y D) x^{2} = - 4 y F) {(x + 1)}^{2} = 4 (y + 1) H) {(x + 1)}^{2} = 4 (y + 1)$