Welcome :: Homework Help and Answers :: Mathskey.com

Recent Visits

  
Welcome to Mathskey.com Question & Answers Community. Ask any math/science homework question and receive answers from other members of the community.

13,435 questions

17,804 answers

1,438 comments

302,623 users

Graphing a Quadratic Inequality. Please help me

0 votes

Sketch the graph of y < 2x2 - 3x.

asked Oct 25, 2013 in ALGEBRA 1 by dkinz Apprentice

1 Answer

0 votes

The inequality is y < 2x 2 - 3x.

Write the equation y = 2x 2 - 3x and it represents a parabola curve.

The graph of the inequality y < 2x 2 - 3x is the shaded region, so every point in the shaded region satisfies the inequality.

The graph of the equation y = 2x 2 - 3x is the boundary of the region. Since the inequality symbol is <, the boundary is drawn as a dotted curve to show that points on the curve doesnot satisfy the inequality.

To graph the boundary curve make the table.

Make the table of values to find ordered pairs that satisfy the equation.

Choose values for x and find the corresponding values for y.

x

y = 2x 2 - 3x

(x, y)

- 1.5

y = 2(- 1.5)2 - 3(- 1.5) = 9

(- 1.5, 9)
- 1

y = 2(- 1)2 - 3(- 1) = 5

(- 1, 5)

0

y = 2(0)2 - 3(0) = 0

(0, 0)

1

y = 2(1)2 - 3(1) = - 1

(1, - 1)

2

y = 2(2)2 - 3(2) = 2

(2, 2)

3

y = 2(3)2 - 3(3) = 9

(3, 9)

To draw inequality y < 2x 2 - 3x follow the steps.

1.  Draw a coordinate plane.

2.  Plot the points and draw a smooth curve through these points.

3.  To determine which side (out side or in side) to be shaded, use a test point inside the parabola. A simple choice is (1, 1).

Substitute the value of (x, y) = (1, 1) in the original inequality.

1 < 2(1) 2 - 3(1)

1 < 2 - 3

1 < - 1.

4.  Since the above statement is false, shade the region outside the parabola.

answered May 31, 2014 by lilly Expert

Related questions

asked Sep 11, 2014 in ALGEBRA 2 by anonymous
...