2. Quadratic Equations, Inequalities, and Functions
Chapter 10
Quadratic Equations, Inequalities,
and Functions

3. Graphs of Quadratic Functions
10.5
Graphs of Quadratic Functions

4. 10.5 Graphs of Quadratic Functions
Objectives
Graph a quadratic function.
Graph parabolas with horizontal and vertical shifts.
Use the coefficient of x2 to predict the shape and direction in which a parabola opens.
Find a quadratic function to model data.
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5. 10.5 Graphs of Quadratic Functions
Graph a Quadratic Function
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6. 10.5 Graphs of Quadratic Functions
Graph Parabolas with Vertical Shifts
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7. 10.5 Graphs of Quadratic Functions
Graph Parabolas with Vertical Shifts
k > 0 produces shift up k units
k < 0 produces shift down k units
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8. 10.5 Graphs of Quadratic Functions
Graph Parabolas with Horizontal Shifts
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9. 10.5 Graphs of Quadratic Functions
Graph Parabolas with Horizontal Shifts
h < 0 produces shift left h units
h > 0 produces shift right h units
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10. 10.5 Graphs of Quadratic Functions
Graph Parabolas with Horizontal and Vertical Shifts
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11. 10.5 Graphs of Quadratic Functions
Graph Parabolas with Horizontal and Vertical Shifts
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12. 10.5 Graphs of Quadratic Functions
Graph Parabolas with Horizontal and Vertical Shifts
Since h < 0, there is a shift to the left, and since k < 0, there is a shift down.
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13. 10.5 Graphs of Quadratic Functions
Graph Parabolas with Horizontal and Vertical Shifts
Axis of symmetry
Vertex
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14. 10.5 Graphs of Quadratic Functions
General Principles of Parabolas
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15. 10.5 Graphs of Quadratic Functions
General Principles of Parabolas
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16. 10.5 Graphs of Quadratic Functions
General Principles of Parabolas
(4, -7)
Shifted right 4 units and down 7 units. Narrower than f (x) = x2.
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17. 10.5 Graphs of Quadratic Functions
Finding a Quadratic Model
The following table shows the higher-order multiple birth rates in the United States since At the right is a scatter diagram of these points.
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18. 10.5 Graphs of Quadratic Functions
Finding a Quadratic Model
We will select three arbitrary ordered pairs to construct our model.
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19. 10.5 Graphs of Quadratic Functions
Finding a Quadratic Model
Selecting three representative ordered pairs, we can write a system of three equations.
Solving these equations using technology, we determine
Choosing different ordered pairs would result in a different model.
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