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5.2 Properties of Parabolas

5.2 Properties of Parabolas. Graphing Parabolas Finding Maximum and Minimum Values. 1) Graphing Parabolas. y = ax 2 + bx + c When b = 0, it becomes… y = ax 2 + c The vertex of a graph of y = ax 2 + c is the y- intercept, (0, c ). 1) Graphing Parabolas. Example 1: Graph.

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5.2 Properties of Parabolas

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  1. 5.2 Properties of Parabolas Graphing Parabolas Finding Maximum and Minimum Values

  2. 1) Graphing Parabolas y = ax2 + bx + c When b = 0, it becomes… y = ax2 + c The vertex of a graph of y = ax2 + c is the y-intercept, (0, c)

  3. 1) Graphing Parabolas Example 1: Graph

  4. 1) Graphing Parabolas Example 1: Graph Step 1: Graph the vertex at (0, -1). Step 2: Make a table of values using points on one side of x-axis. Step 3: Sketch the curve.

  5. 1) Graphing Parabolas Example 1: Graph

  6. 1) Graphing Parabolas Example 1: Graph

  7. 1) Graphing Parabolas Take advantage of corresponding points to graph the other side of the parabola. Example 1: Graph

  8. 1) Graphing Parabolas For the equation y = ax2 + bx + c, the axis of symmetry is at

  9. 1) Graphing Parabolas Example 2: Graph y = x2 – 2x – 3.

  10. 1) Graphing Parabolas Example 2: Graph y = x2 – 2x – 3. Step 1: Find the axis of symmetry. Axis of symmetry: Equation for the axis of symmetry: x = 1

  11. 1) Graphing Parabolas Example 2: Graph y = x2 – 2x – 3. Step 2: Find the vertex. Sub x = 1into the equation, solve for y. y = (1)2 – 2(1) – 3 y = -4 The vertex is at (1, -4).

  12. 1) Graphing Parabolas Example 2: Graph y = x2 – 2x – 3. Step 3: Plot points and sketch the graph.

  13. 1) Graphing Parabolas Example 2: Graph y = x2 – 2x – 3. Step 3: Plot points and sketch the graph.

  14. 1) Graphing Parabolas Example 2: Graph y = x2 – 2x – 3.

  15. 2) Finding Maximum and Minimum Values The maximum or minimum occurs at the vertex.. If a < 0, the graph opens DOWN and the vertex is a MAXIMUM. If a > 0, the graph opens UP and the vertex is a MINIMUM.

  16. Homework p. 248 #1-3, 10-12, 22-24, 31, 37-39, 45

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