Y < -x^2+6x-12 graphed, and shade the side that needs to be shaded?

Question

graph y < -x^2+6x-12 and shade the side that needs to be shaded (you can just tell me what to do and give me the coordinates :)

Answer 1

The inequality is y < - x² + 6x -12.

Write the equality is y = - x² + 6x -12 and it is represent parabola curve.

The graph of the inequality y < - x² + 6x -12 is the shaded region, so every point in the shaded region satisfies the inequality.

The graph of the equation y = - x² + 6x -12 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 does not satisfy the inequality and the shaded region of the graph of y = - x² + 6x -12 is the soutions to the inequaity.

To graph the boundary curve make the table of values to find ordered pairs that satisfy the equation.

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

x	y = - x2 + 6x - 12	(x, y )
- 2	y = - (- 2)2 + 6(- 2) -12 = - 28	(- 2, - 28)
- 1	y = - (- 1)2 + 6(- 1) -12 =  - 19	(- 1, - 19)
0	y = - (0)2 + 6(0) -12 = - 12	(0, - 12)
1	y = - (1)2 + 6(1) -12 = - 7	(1, - 7)
2	y = - (2)2 + 6(2) -12 =  - 4	(2, - 4)
3	y = - (3)2 + 6(3) -12 =  - 3	(3, - 3)
4	y = - (4)2 + 6(4) -12 =  - 4	(4, - 4)
5	y = - (5)2 + 6(5) -12 = - 7	(5, - 7)
6	y = - (6)2 + 6(6) -12 = - 12	(6, -12)
8	y = - (8)2 + 6(8) -12 = - 28	(8, -28)

To draw inequality y < - x² + 6x -12 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 (3, -8).

Substitute the value of (x, y) = (3, -8) in the original inequality.

- 8 < - (3)² + 6(3) -12

- 8 < - 3

4.  Since the above statement is true, shade the region  inside the parabola.