Math 10.1
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Math 10.1 Math 10.1 Presentation Transcript

  • Section 10.1GRAPH y = ax2 +cI will graph simple quadratic functions.
  • Quadratic Functionnon linear functionthat can be written in standard form, y = ax2 + bx + c
  • Quadratic Parabola Function U-shaped graph thatnon linear function a quadratic functionthat can be written makes in standard form, y = ax2 + bx + c
  • Quadratic Parabola Function U-shaped graph thatnon linear function a quadratic functionthat can be written makes in standard form, y = ax2 + bx + c
  • Quadratic Parabola Vertex Function U-shaped graph that the lowest or highestnon linear function a quadratic function point on a parabolathat can be written makes in standard form, y = ax2 + bx + c
  • Quadratic Parabola Vertex Function U-shaped graph that the lowest or highestnon linear function a quadratic function point on a parabolathat can be written makes in standard form, y = ax2 + bx + c
  • Quadratic Parabola Vertex Function U-shaped graph that the lowest or highestnon linear function a quadratic function point on a parabolathat can be written makes The vertex of the in standard form, parent equation y = ax2 + bx + c y = x2 is (0,0)
  • Quadratic Parabola Vertex Function U-shaped graph that the lowest or highestnon linear function a quadratic function point on a parabolathat can be written makes The vertex of the in standard form, parent equation y = ax2 + bx + c y = x2 is (0,0)
  • Quadratic Parabola Vertex Function U-shaped graph that the lowest or highestnon linear function a quadratic function point on a parabolathat can be written makes The vertex of the in standard form, parent equation y = ax2 + bx + c y = x2 is (0,0)
  • Quadratic Parabola Vertex Function U-shaped graph that the lowest or highestnon linear function a quadratic function point on a parabolathat can be written makes The vertex of the in standard form, parent equation y = ax2 + bx + c y = x2 is (0,0) Parent Quadratic Function the most basic quadratic equation, y = x2
  • Quadratic Parabola Vertex Function U-shaped graph that the lowest or highestnon linear function a quadratic function point on a parabolathat can be written makes The vertex of the in standard form, parent equation y = ax2 + bx + c y = x2 is (0,0) Axis of Symmetrythe line that passes through the vertex and divides the parabola in two symmetrical parts. The a of s of y = x2 is x=0 Parent Quadratic Function the most basic quadratic equation, y = x2
  • Quadratic Parabola Vertex Function U-shaped graph that the lowest or highestnon linear function a quadratic function point on a parabolathat can be written makes The vertex of the in standard form, parent equation y = ax2 + bx + c y = x2 is (0,0) Axis of Symmetrythe line that passes through the vertex and divides the parabola in two symmetrical parts. The a of s of y = x2 is x=0 Parent Quadratic Function the most basic quadratic equation, y = x2
  • Quadratic Parabola Vertex Function U-shaped graph that the lowest or highestnon linear function a quadratic function point on a parabolathat can be written makes The vertex of the in standard form, parent equation y = ax2 + bx + c y = x2 is (0,0) Axis of Symmetrythe line that passes through the vertex and divides the parabola in two symmetrical parts. The a of s of y = x2 is x=0 Parent Quadratic Function the most basic quadratic equation, y = x2
  • Example 1
  • ★Step 1: Example 1Make a table ofvalues
  • ★Step 1: Example 1Make a table ofvalues★Step 2:Plot the pointsfrom the tables
  • ★Step 1: Example 1Make a table ofvalues★Step 2:Plot the pointsfrom the tables★Step 3:Draw a smoothcurve throughthe points
  • ★Step 1: Example 1Make a table ofvalues★Step 2:Plot the pointsfrom the tables★Step 3:Draw a smoothcurve throughthe points★Step 4:Compare thegraphs (vertex,axis of symmetry,vertical stretch)
  • Example 1
  • ★Step 1: Example 1Make a table ofvalues
  • ★Step 1: Example 1Make a table ofvalues★Step 2:Plot the pointsfrom the tables
  • ★Step 1: Example 1Make a table ofvalues★Step 2:Plot the pointsfrom the tables★Step 3:Draw a smoothcurve throughthe points
  • ★Step 1: Example 1Make a table ofvalues★Step 2:Plot the pointsfrom the tables★Step 3:Draw a smoothcurve throughthe points★Step 4:Compare thegraphs (vertex,axis of symmetry,vertical stretch)
  • Graph y = 1/2x2. Compare theExample 2 graph with the graph of y = x2
  • Graph y = 1/2x2. Compare the★Step 1: Example 2 graph with the graph of y = x2Make a table ofvalues
  • Graph y = 1/2x2. Compare the★Step 1: Example 2 graph with the graph of y = x2Make a table ofvalues★Step 2:Plot the pointsfrom the tables
  • Graph y = 1/2x2. Compare the★Step 1: Example 2 graph with the graph of y = x2Make a table ofvalues★Step 2:Plot the pointsfrom the tables★Step 3:Draw a smoothcurve throughthe points
  • Graph y = 1/2x2. Compare the★Step 1: Example 2 graph with the graph of y = x2Make a table ofvalues★Step 2:Plot the pointsfrom the tables★Step 3:Draw a smoothcurve throughthe points★Step 4:Compare thegraphs (vertex,axis of symmetry,vertical stretch)
  • Example 2
  • ★Step 1: Example 2Make a table ofvalues
  • ★Step 1: Example 2Make a table ofvalues★Step 2:Plot the pointsfrom the tables
  • ★Step 1: Example 2Make a table ofvalues★Step 2:Plot the pointsfrom the tables★Step 3:Draw a smoothcurve throughthe points
  • ★Step 1: Example 2Make a table ofvalues★Step 2:Plot the pointsfrom the tables★Step 3:Draw a smoothcurve throughthe points★Step 4:Compare thegraphs (vertex,axis of symmetry,vertical stretch)
  • Comparing to y=x 2When |a|>1, then there is a vertical stretch, by a factor of a.When |a|<1, then there is a vertical shrink, by a factor of a. When a is negative, whether a>1 or a<1, then there is a reflection in the x-axis.
  • Example 3
  • Example 3
  • Example 4
  • Example 4
  • Comparing to y=x 2 When |a|>1, then there is a vertical stretch, by a factor of a. When |a|<1, then there is a vertical shrink, by a factor of a.When a is negative, whether a>1 or a<1, then there is a reflection in the x-axis.When c is positive, then there is a vertical translation up c units.When c is negative, then there is a vertical translation down c units.
  • Example 5
  • Example 5
  • Example 6
  • Example 6
  • Page 632# 3-5,6,10,14,18,22,23,24,27,33,37