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WARM UP

WARM UP. 4. Simplify 6 2 (-14) 2 -9 2 -4x 2 , for x = 3. WARM UP. 3. Simplify 6 2 (-14) 2 -9 2 -4x 2 , for x = 3. WARM UP. 2. Simplify 6 2 (-14) 2 -9 2 -4x 2 , for x = 3. WARM UP. 1. Simplify 6 2 (-14) 2 -9 2 -4x 2 , for x = 3. WARM UP. 0. Simplify 6 2 (-14) 2 -9 2

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WARM UP

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  1. WARM UP 4 Simplify 62 (-14)2 -92 -4x2, for x = 3

  2. WARM UP 3 Simplify 62 (-14)2 -92 -4x2, for x = 3

  3. WARM UP 2 Simplify 62 (-14)2 -92 -4x2, for x = 3

  4. WARM UP 1 Simplify 62 (-14)2 -92 -4x2, for x = 3

  5. WARM UP 0 Simplify 62 (-14)2 -92 -4x2, for x = 3

  6. 9.4 Graphing Quadratic Functions A quadratic function is a function that can be written in the standard form y = ax2 + 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.

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

  8. EXAMPLE 1 Describe the Graph of a Parabola The graph of y = x2 opens up. The lowest point is (0, 0). The graph of y = –x2 + 4 opens down. The highest point is (0, 4). 9.4 Graphing Quadratic Functions

  9. 9.4 Graphing Quadratic Functions Checkpoint Describe the Graph of a Parabola Decide whether the parabola opens up or down. y = -x2 y = 2x2 - 4 y = -3x2 + 5x - 1

  10. 9.4 Graphing Quadratic Functions 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.

  11. 9.4 Graphing Quadratic Functions GRAPHING A QUADRATIC FUNCTION The graph of y = ax2 + bx + c is a parabola. STEP 1 Find the x-coordinate of the vertex, which is x = - STEP 2 Make a table of values, using x-values to the left and right of the vertex. STEP 3 Plot the points and connect them with a smooth curve to form a parabola.

  12. EXAMPLE 2Graph Quadratic Function with Positive a-Value Sketch the graph of y = x2 - 2x – 3 SOLUTION In this quadratic function, a =1, b = -2, and c = -3. STEP 1 Find the x-coordinate of the vertex - = = 1 9.4 Graphing Quadratic Functions

  13. EXAMPLE 2Graph Quadratic Function with Positive a-Value Sketch the graph of y = x2 - 2x – 3 SOLUTION In this quadratic function, a =1, b = -2, and c = -3. STEP 2 Make a table of values, using x-values to the left and right of x=1 9.4 Graphing Quadratic Functions

  14. EXAMPLE 2Graph Quadratic Function with Positive a-Value Sketch the graph of y = x2 - 2x – 3 SOLUTION In this quadratic function, a =1, b = -2, and c = -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. 9.4 Graphing Quadratic Functions Checkpoint Graph a Quadratic Function with a Positive a-Value Sketch the graph of the function. Label the coordinates of the vertex. y = x2 + 2 y = 2x2 – 4x - 1 y = x2+ 2x

  16. EXAMPLE 3Graph Quadratic Function with Negative a-Value Sketch the graph of y = -x2 - 3x +1 SOLUTION In this quadratic function, a =-1, b = -3, and c = 1. STEP 1 Find the x-coordinate of the vertex - = = - or -1.5 9.4 Graphing Quadratic Functions

  17. EXAMPLE 2Graph Quadratic Function with Negative a-Value Sketch the graph of y = -x2 - 3x + 1 SOLUTION In this quadratic function, a =-1, b = -3, and c = 1. STEP 2 Make a table of values, using x-values to the left and right of x=1 9.4 Graphing Quadratic Functions

  18. EXAMPLE 2Graph Quadratic Function with Negative a-Value Sketch the graph of y = -x2 - 3x + 1 SOLUTION In this quadratic function, a =-1, b = -3, and c = 1. 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 = -x2 - 3x + 1, let x = 0. The y-intercept is 1. 9.4 Graphing Quadratic Functions

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

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