Chapter 10: Q 13. (page 643)

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

Short Answer

Expert verified

The correct match is (E).

Step by step solution

Step 1. Given information.

We have given graph is,

and given equations are $A) y^{2} = 4 x C) y^{2} = - 4 x E) {(y - 1)}^{2} = 4 (x - 1) G) {(y - 1)}^{2} = - 4 (x - 1) B) x^{2} = 4 y D) x^{2} = - 4 y F) {(x + 1)}^{2} = 4 (y + 1) H) {(x + 1)}^{2} = 4 (y + 1)$

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,

and vertex of the parabola is (1, 1).

this graph is the parabola opens to right.

Using equation of the parabola and vertex,

${(y - k)}^{2} = 4 a (x - h) \Rightarrow {(y - 1)}^{2} = 4 a (x - 1)$

Graph is opens to the right hence so a is positive (a > 0).

Therefore equation ${(y - 1)}^{2} = 4 (x - 1)$

is the equation of given graph.

Step 4. Conclusion.

Hence, equation of the graph

is ${(y - 1)}^{2} = 4 (x - 1)$ .

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

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.A)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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Study anywhere. Anytime. Across all devices.

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