1. Warm Up
Evaluate (plug the x values into the expression) x2 + 5x for x = 4 and x = –3.
2. Generate ordered pairs for the function y = x2 + 2 with the given domain.
D: {–2, –1, 0, 1, 2}

2. The function y = x2 A quadratic function is any function that can be written in the standard form y = ax2 + bx + c,

3. Example 1B: Identifying Quadratic Functions
Tell whether the functions are quadratic. Explain.
y = 7x + 3
y = x2 + 4x – 3
y = x2 – 8

4. Example 1C: Identifying Quadratic Functions
Tell whether the function is quadratic. Explain.
y – 10x2 = 9
y + 4 = x
2y = 4x2 + 8

5. The graph of a quadratic function is a curve called a parabola
The graph of a quadratic function is a curve called a parabola. To graph a quadratic function, generate enough ordered pairs to see the shape of the parabola. Then connect the points with a smooth curve.

6. Example 2A: Graphing Quadratic Functions by Using a Table of Values
Use a table of values to graph the quadratic function. x y –2 –1 1 2

7. Example 2B: Graphing Quadratic Functions by Using a Table of Values
Use a table of values to graph the quadratic function.
y = –4x2 x –2 –1 1 2

8. Check It Out! Example 2a
Use a table of values to graph each quadratic function.
y = x2 + 2

9. Check It Out! Example 2b
Use a table of values to graph the quadratic function.
y = –3x2 + 1

10. y = ax2 + bx + c, the value of a determines the direction a parabola opens.
A parabola opens upward when a > 0.
A parabola opens downward when a < 0.

11. Check It Out! Example 3a
Tell whether the graph of the quadratic function opens upward or downward. Explain.
f(x) = –4x2 – x + 1

12. Example 3A: Identifying the Direction of a Parabola
Tell whether the graph of the quadratic function opens upward or downward. Explain.

13. Example 3B: Identifying the Direction of a Parabola
Tell whether the graph of the quadratic function opens upward or downward. Explain.
y = 5x – 3x2

14. The highest or lowest point on a parabola is the vertex
The highest or lowest point on a parabola is the vertex. If a parabola opens upward, the vertex is the lowest point. If a parabola opens downward, the vertex is the highest point.

16. Example 4: Identifying the Vertex and the Minimum or Maximum
Identify the vertex of each parabola. Then give the minimum or maximum value of the function. A. B.

17. Check It Out! Example 4
Identify the vertex of each parabola. Then give the minimum or maximum value of the function. a. b.

18. A vertical line that divides a parabola into two symmetrical halves is the axis of symmetry. The axis of symmetry always passes through the vertex of the parabola.

19. Example 2: Finding the Axis of Symmetry by Using Zeros
Find the axis of symmetry of each parabola. A.
The axis of symmetry is x = ? B.
The axis of symmetry is x = ?

20. Check It Out! Example 2
Find the axis of symmetry of each parabola. a.
The axis of symmetry is b.
The axis of symmetry is

21. Unless a specific domain is given, you may assume that the domain of a quadratic function is all real numbers. You can find the range of a quadratic function by looking at its graph.
For the graph of y = x2 – 4x + 5, the range begins at the minimum value of the function, where y = 1. All the y-values of the function are greater than or equal to 1. So the range is y  1.

22. Example 5: Finding Domain and Range
Find the domain and range.
Step 1 The graph opens downward, so identify the maximum.
Step 2 Find the domain and range.

23. Check It Out! Example 5a
Find the domain and range.
Step 1 The graph opens upward, so identify the minimum.
Step 2 Find the domain and range.

24. Check It Out! Example 5b
Find the domain and range.