Question

how do you solve this quadratic equation.y >/= x^2-3x+1.

Answer 1

The inequality is y ≥ x² - 3x +1.

Write the equality is y = x² - 3x +1 and it is represent parabola curve.

The graph of the inequality y ≥ x² - 3x +1 is the shaded region, so every point in the shaded region satisfies the inequality.

The graph of the equation y = x² - 3x +1 is the boundary of the region. Since the inequality symbol is ≥, the boundary is drawn as a solid curve to show that points on the curve does satisfy the inequality and the shaded region above the graph of y = x² - 3x +1.

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 = x2 - 3x +1	(x, y)
- 2	y = (- 2)2 - 3(- 2) +1 = 4 + 6 +1 = 11	(- 2, 11)
- 1	y = (- 1)2 - 3(- 1) +1 = 1 + 3 +1 = 5	(- 1, 5)
0	y = (0)2 - 3(0) +1 = 0 - 0 +1 = 1	(0, 1)
1	y = (1)2 - 3(1) +1 = 1 - 3 +1 = - 1	(1, - 1)
2	y = (2)2 - 3(2) +1 = 4 - 6 +1 = - 1	(2, - 1)
3	y = (3)2 - 3(3) +1 = 9 - 9 +1 = 1	(3, 1)
4	y = (4)2 - 3(4) +1 = 16 - 12 +1 = 5	(4, 5)
5	y = (5)2 - 3(5) +1 = 25 - 15 +1 = 11	(5, 11)

To draw inequality y ≥ x² - 3x +1 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) ≥ (1)² - 3(1) +1

1 ≥ 1 - 3 +1

0 ≥ - 3.

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