Chapter 11: Q.267 (page 1156)

In the following exercises, graph each equation by using its properties: $y = - x^{2} + 10 x$

Short Answer

Expert verified

The graph can be given as

Step by step solution

Given information

We are given an equation of parabola $y = - x^{2} + 10 x$

Find out whether the parabola is upward or downward

As the coefficient of $x^{2}$ is negative the parabola is downward

Axis of symmetry

To find the axis of symmetry put

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

Substituting the values we get

role="math" localid="1645498573688" $x = - \frac{10}{- 2} x = 5$

Find the vertex of the parabola

To find the vertex we put $x = 5$ in the equation

we get,

$y = - x^{2} + 10 x y = - {(5)}^{2} + 10 (5) y = - 25 + 50 y = 25$

Find the y-intercept

To find y-intercept put $x = 0$

we get,

$y = - x^{2} + 10 x y = - {(0)}^{2} + 10 (0) y = 0$

As this coordinate is 5 units left to the axis of symmetry there is a coordinate 5 units right to the parabola which can be given as $(10, 0)$

The coordinate is $(0, 0)$

Find the x-intercept

To find x-intercept put $y = 0$

$- x^{2} + 10 x = 0 x^{2} - 10 x = 0 x (x - 10) = 0 x = 0 o r x = 10$

Hence the coordinates are $(0, 0), (10, 0)$

Plot the graph of parabola

The graph of parabola can be given as

Conclusion

The graph can be given as

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In the following exercises, graph each equation by using its properties: $y = - x^{2} + 10 x$

Short Answer

Step by step solution

Given information

Find out whether the parabola is upward or downward

Axis of symmetry

Find the vertex of the parabola

Find the y-intercept

Find the x-intercept

Plot the graph of parabola

Conclusion

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Most popular questions from this chapter

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Study anywhere. Anytime. Across all devices.

In the following exercises, graph each equation by using its properties: y=-x2+10x

Short Answer

Step by step solution

Given information

Find out whether the parabola is upward or downward

Axis of symmetry

Find the vertex of the parabola

Find the y-intercept

Find the x-intercept

Plot the graph of parabola

Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Discrete Mathematics

Theoretical and Mathematical Physics

Statistics

Geometry

Mechanics Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, graph each equation by using its properties: $y = - x^{2} + 10 x$