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Lesson 5.1 AIM: Finding the Vertex and Axis of Symmetry for a Parabola

Lesson 5.1 AIM: Finding the Vertex and Axis of Symmetry for a Parabola. This Parabola has a minimum. This Parabola has a maximum. Vertex. A vertex is either a maximum or a minimum of a parabola. Axis of Symmetry. The axis of symmetry is the line that runs down the middle of a parabola.

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Lesson 5.1 AIM: Finding the Vertex and Axis of Symmetry for a Parabola

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  1. Lesson 5.1AIM: Finding the Vertex and Axis of Symmetry for a Parabola

  2. This Parabola has a minimum.

  3. This Parabola has a maximum.

  4. Vertex • A vertex is either a maximum or a minimum of a parabola.

  5. Axis of Symmetry • The axis of symmetry is the line that runs down the middle of a parabola. • It cuts the parabola in half.

  6. Standard Form: ax2 + bx + c • What does the “a” do? • “a” determines how fat or skinny the parabola is. • As “a” gets bigger, the parabola gets skinnier!

  7. Standard Form: ax2 + bx + c • What if “a” is positive? • The parabola has a minimum - or the parabola has a “smiley” face • What if “a” is negative? • The parabola has a maximum - or the parabola has a “frowny” face

  8. Standard Form: ax2 + bx + c • What does “c” do? • The “c” determines the y-intercept

  9. Finding the Vertex and Axis of Symmetry using a Graph. Vertex: (-2 , -3) Axis of Symmetry: x = -2

  10. Finding the vertex using the equation y = x2 - 2x - 5 STEP 1: Determine “a”, “b”, and “c” a = 1 b = -2 c = -5

  11. Finding the vertex using the equation y = x2 - 2x - 5 STEP 2: Find the axis of symmetry using x = (-b/2a)

  12. Finding the vertex using the equation y = x2 - 2x - 5 STEP 3: Plug x value back into original equation to solve for y. x = 1 y = (1)2 - 2(1) - 5 = 1 - 2 - 5 = -6 Vertex = (1, -6)

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