1. DÉJÀ VU: Graphing Linear Inequalities
Graph the inequality
The boundary line is which has a y-int of (0, 2) and a slope of .
Draw the boundary line dashed because it is not part of the solution.
Then shade the region above the boundary line to show .

2. Earlier we solved linear inequalities in two variables by graphing
Earlier we solved linear inequalities in two variables by graphing. We can use a similar procedure to graph quadratic inequalities.

3. Notes For A) f(x)= -x2 + 7 B) f(x)= x2 + 8x - 20 C) f(x)= -2(x-3)2 +7
Identify the vertex, and state the domain and range
2. For y > (x+1)2 – 3
A. State shifts B. Find vertex
C. Graph (and shade)
3. For y > -x2 – 4x
A. Up or downward B. Find vertex
C. Graph (and shade)
4. For y ≤ x2 + 9x + 14
A. Up or downward B. Find vertex
C. Find y-intercept D. Graph (and shade)

4. Notes
Identify the vertex, state the domain and range for A) f(x)= -x2 + 7
B) f(x)= x2 + 8x – 20
C) f(x)= -2(x-3)2 +7
2. For y = (x+1)2 – 3
A. State shifts B. Find vertex
C. Graph y > (x+1)2 – 3
(and shade)

5. Example 1: Graphing Quadratic Inequalities in Two Variables
Graph y ≥ x2 – 7x + 10.
Step 1 Graph the boundary of the related parabola y = x2 – 7x + 10 with a solid curve. Its y-int is (0,10), its vertex is (3.5, –2.25).

6. Example 1 Continued
Step 2 Shade above the parabola because the solution consists of y-values greater than those on the parabola for corresponding x-values.

7. Example 2
Graph the inequality.
y ≥ 2x2 – 5x – 2
Step 1 Graph the boundary of the related parabola y = 2x2 – 5x – 2 with a solid curve. Its y-int is (0,–2), its vertex is (1.3, –5.1).

8. Example 2 Continued
Step 2 Shade above the parabola because the solution consists of y-values greater than those on the parabola for corresponding x-values.

9. Example 3
Graph each inequality.
y < –3x2 – 6x – 7
Step 1 Graph the boundary of the related parabola y = –3x2 – 6x – 7 with a dashed curve. Its y-intercept is (0, –7).

10. Example 3 Continued
Step 2 Shade below the parabola because the solution consists of y-values less than those on the parabola for corresponding x-values.

11. Notes
3. For y > -x2 – 4x
A. Up or downward
B. Find vertex
C. Graph (and shade)
4. For y ≤ x2 + 9x + 14
A. Up or downward
B. Find vertex
C. Find y-intercept
D. Graph (and shade)

12. Notes
4. For y ≤ x2 + 9x + 14
A. State whether it opens upward or downward
B. Find the vertex
C. Find the y-intercept
D. Graph the boundary line
E. Shade