1. WARM UP Simplify 1.6 2 2.(-14) 2 3.-9 2 4.-4x 2, for x = 3 4

2. WARM UP Simplify 1.6 2 2.(-14) 2 3.-9 2 4.-4x 2, for x = 3 3

3. WARM UP Simplify 1.6 2 2.(-14) 2 3.-9 2 4.-4x 2, for x = 3 2

4. WARM UP Simplify 1.6 2 2.(-14) 2 3.-9 2 4.-4x 2, for x = 3 1

5. Simplify 1.6 2 2.(-14) 2 3.-9 2 4.-4x 2, for x = 3 WARM UP 0

6. A quadratic function is a function that can be written in the standard form y = ax 2 + bx + c Every quadratic function has a U-shaped graph called a parabola. The parabola opens up if the value of a is positive. The parabola opens down if the value of a is negative. 9.4 Graphing Quadratic Functions

7. GOAL Sketch the graph of a quadratic function KEY WORDS Quadratic function Parabola Vertex Axis of symmetry 9.4 Graphing Quadratic Functions

8. EXAMPLE 1 EXAMPLE 1 Describe the Graph of a Parabola a)The graph of y = x 2 opens up. The lowest point is (0, 0). b)The graph of y = –x 2 + 4 opens down. The highest point is (0, 4). 9.4 Graphing Quadratic Functions

9. Checkpoint Describe the Graph of a Parabola Decide whether the parabola opens up or down. 1.y = -x 2 2.y = 2x 2 - 4 3.y = -3x 2 + 5x - 1 9.4 Graphing Quadratic Functions

10. The vertex is the highest or lowest point on a parabola. The vertical line passing through the vertex that divides the parabola into two symmetric parts is called the axis of symmetry. The two symmetric parts are mirror images of each other. 9.4 Graphing Quadratic Functions

11. GRAPHING A QUADRATIC FUNCTION The graph of y = ax 2 + bx + c is a parabola. 1 STEP 1 Find the x-coordinate of the vertex, which is x = - 2 STEP 2 Make a table of values, using x-values to the left and right of the vertex. 3 STEP 3 Plot the points and connect them with a smooth curve to form a parabola. 9.4 Graphing Quadratic Functions

12. EXAMPLE 2 EXAMPLE 2 Graph Quadratic Function with Positive a-Value Sketch the graph of y = x 2 - 2x – 3 SOLUTION In this quadratic function, a =1, b = -2, and c = -3. 1 STEP 1 Find the x-coordinate of the vertex - = = 1 9.4 Graphing Quadratic Functions

13. EXAMPLE 2 EXAMPLE 2 Graph Quadratic Function with Positive a-Value Sketch the graph of y = x 2 - 2x – 3 SOLUTION In this quadratic function, a =1, b = -2, and c = -3. 2 STEP 2 Make a table of values, using x-values to the left and right of x=1 9.4 Graphing Quadratic Functions x-201234 y

14. EXAMPLE 2 EXAMPLE 2 Graph Quadratic Function with Positive a-Value Sketch the graph of y = x 2 - 2x – 3 SOLUTION In this quadratic function, a =1, b = -2, and c = -3. 3 STEP 3 Plot the points. The vertex is (1, -4). Connect the points to form a parabola that opens up since a is positive. The axis of symmetry passes through the vertex. The x-coordinate of the vertex is 1, and the axis of symmetry is the vertical line x = 1. 9.4 Graphing Quadratic Functions

15. Checkpoint Graph a Quadratic Function with a Positive a-Value Sketch the graph of the function. Label the coordinates of the vertex. 1.y = x 2 + 2 2.y = 2x 2 – 4x - 1 3.y = x 2 + 2x 9.4 Graphing Quadratic Functions

16. EXAMPLE 3 EXAMPLE 3 Graph Quadratic Function with Negative a-Value Sketch the graph of y = -x 2 - 3x + 1 SOLUTION In this quadratic function, a =-1, b = -3, and c = 1. 1 STEP 1 Find the x-coordinate of the vertex - = = - or -1.5 9.4 Graphing Quadratic Functions

17. EXAMPLE 2 EXAMPLE 2 Graph Quadratic Function with Negative a-Value Sketch the graph of y = -x 2 - 3x + 1 SOLUTION In this quadratic function, a =-1, b = -3, and c = 1. 2 STEP 2 Make a table of values, using x-values to the left and right of x=1 9.4 Graphing Quadratic Functions x-4-3-2-1.501 y

18. EXAMPLE 2 EXAMPLE 2 Graph Quadratic Function with Negative a-Value Sketch the graph of y = -x 2 - 3x + 1 SOLUTION In this quadratic function, a =-1, b = -3, and c = 1. 3 STEP 3 Plot the points. The vertex is (-1.5, 3.25). Connect the points to form a parabola that opens down since a is negative. To find the y-intercept of y = -x 2 - 3x + 1, let x = 0. The y-intercept is 1. 9.4 Graphing Quadratic Functions

19. YOU’RE CERTIFIED! Page 523 #s 15 -32 9.4 Graphing Quadratic Functions