Chapter 11: Q.269 (page 1069)

In the following exercise a) write the equation in standard form b) use properties of standard form to graph the parabola:
$y = 2 x^{2} - 4 x - 2$

Short Answer

Expert verified

The equation in standard form can be given as $y = 2 {(x - 1)}^{2} - 4$

The graph of the parabola is

Step by step solution

Given information

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

Write the equation in standard form

We have,

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

Comparing with standard form we get a=2, h=1,k=-4

Find the axis of symmetry and vertex of parabola

To find the axis of symmetry we use $x = h$

we get $x = 1$

The vertex of parabola can be given as $(h, k) = (1, - 4)$

Find y-intercept

To find y-intercept put $x = 0$

we get,

role="math" localid="1645500719954" $y = 2 {(x - 1)}^{2} - 4 y = 2 {(- 1)}^{2} - 4 y = 2 - 4 y = - 2$

Find the point of symmetry to (0,-2) across the axis of symmetry

The point of symmetry can be given as $(2, - 2)$

Find the x-intercept

To find x-intercept put $y = 0$

We get,

localid="1667921246558" $2 {(x - 1)}^{2} - 4 = 0 {(x - 1)}^{2} = 2 x - 1 = \pm \sqrt{2} x = 1 \pm \sqrt{2}$

Hence the coordinates are $(1 + \sqrt{2}, 0), (1 - \sqrt{2}, 0)$

Plot the graph of the parabola

The graph can be given as

Conclusion

The equation in standard form can be given as $y = 2 {(x - 1)}^{2} - 4$

The graph can be given as

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In the following exercise a) write the equation in standard form b) use properties of standard form to graph the parabola:
$y = 2 x^{2} - 4 x - 2$

Short Answer

Step by step solution

Given information

Write the equation in standard form

Find the axis of symmetry and vertex of parabola

Find y-intercept

Find the point of symmetry to (0,-2) across the axis of symmetry

Find the x-intercept

Plot the graph of the parabola

Conclusion

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In the following exercise a) write the equation in standard form b) use properties of standard form to graph the parabola:y=2x2-4x-2

Short Answer

Step by step solution

Given information

Write the equation in standard form

Find the axis of symmetry and vertex of parabola

Find y-intercept

Find the point of symmetry to (0,-2) across the axis of symmetry

Find the x-intercept

Plot the graph of the parabola

Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Calculus

Decision Maths

Applied Mathematics

Statistics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

In the following exercise a) write the equation in standard form b) use properties of standard form to graph the parabola:
$y = 2 x^{2} - 4 x - 2$