Chapter 11: Q.274 (page 1156)

In the following exercise graph each equation by using its properties: $x = - y^{2} + 2 y + 4$

Short Answer

Expert verified

The graph can be given as

Step by step solution

Given information

We are given a equation $x = - y^{2} + 2 y + 4$

Check whether the parabola opens to right or left

As the coefficient of the square term is negative the parabola opens to the Left

Find the axis of symmetry

To find the axis of symmetry calculate

$y = - \frac{b}{2 a} y = - \frac{2}{- 2} y = 1$

Find the vertex of parabola

To find the vertex put $y = 1$ in the equation

we get,

$x = - 1 + 2 + 4 x = 5$

The vertex of the parabola is $(5, 1)$

Find y-intercept

To find x-intercept put $y = 0$

we get

$x = 0 + 0 + 4 x = 4$

The coordinate is $(4, 0)$

Find y-intercept

Put $y = 0$

we get,

$x = 0 + 0 + 4 x = 4$

On solving using the quadratic formula we get $x = 3.236 o r x = - 1.236$

Hence the coordinates are

$(0, 3.236), (0, - 1.236)$

Plot the graph

The graph of parabola can be given as

Conclusion

The graph of the parabola is

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In the following exercise graph each equation by using its properties: $x = - y^{2} + 2 y + 4$

Short Answer

Step by step solution

Given information

Check whether the parabola opens to right or left

Find the axis of symmetry

Find the vertex of parabola

Find y-intercept

Find y-intercept

Plot the graph

Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

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Study anywhere. Anytime. Across all devices.

In the following exercise graph each equation by using its properties:x=-y2+2y+4

Short Answer

Step by step solution

Given information

Check whether the parabola opens to right or left

Find the axis of symmetry

Find the vertex of parabola

Find y-intercept

Find y-intercept

Plot the graph

Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Probability and Statistics

Pure Maths

Geometry

Applied Mathematics

Calculus

Study anywhere. Anytime. Across all devices.

In the following exercise graph each equation by using its properties: $x = - y^{2} + 2 y + 4$