Chapter Summary and Review continued
9.7
Examples on
pp. 540–542
USING THE DISCRIMINANT
You can use the discriminant, b2 4ac, to find the number of
solutions of a quadratic equation in the standard form ax2 bx c 0. A
positive value indicates two solutions, zero indicates one solution, and a negative
value indicates no real solution. The value of the discriminant can also be used to
find the number of x-intercepts of the graph of y ax2 bx c.
EXAMPLE
EQUATION
DISCRIMINANT
NUMBER OF SOLUTIONS
3x2 6x 2 0
(6)2 4(3)(2) 12
2
2x 8x 8 0
8 4(2)(8) 0
1
x2 7x 15 0
72 4(1)(15) 11
0
2
2
Determine whether the equation has two solutions, one solution, or
no real solution.
22. 3x2 12x 12 0
23. 2x2 10x 6 0
24. x2 3x 5 0
Find the number of x-intercepts of the graph of the function.
25. y 2x2 3x 1
9.8
26. y x2 3x 3
27. y x2 2x 1
Examples on
pp. 547–549
GRAPHING Q UADRATIC INEQUALITIES
EXAMPLE
Sketch the graph of y < x2 9.
Sketch the graph of y x2 9 that corresponds to y < x2 9.
b
The x-coordinate of the vertex is , or 0. Make a table of values, using x-values
2a
to the left and right of x 0
x
3
2
1
0
1
2
3
y
0
5
8
9
8
5
0
Plot the points and connect them with a smooth
curve to form a parabola. Use a dashed line
since the inequality contains the symbol <.
Shade the region below the parabola because
the inequality states that y is less than x2 9.
y
6
2
4 x
y < x2 9
Sketch the graph of the inequality.
28. y ≤ x2 4
556
Chapter 9
29. y ≥ x2 2x 3
Quadratic Equations and Functions
30. y > 2x2 4x 6