# 10.1 & 10.2: Exploring Quadratic Graphs and Functions - PowerPoint PPT Presentation

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10.1 & 10.2: Exploring Quadratic Graphs and Functions. Objective: To graph quadratic functions. Review:. Linear Equations? Quadratic Equations? Exponential Equations?. Activity:. Graph: y=x 2 and y=3x 2 on the same coordinate plane. How are they the same? How are they different?

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10.1 & 10.2: Exploring Quadratic Graphs and Functions

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## 10.1 & 10.2: Exploring Quadratic Graphs and Functions

### Review:

Linear Equations?

Exponential Equations?

### Activity:

• Graph: y=x2 and y=3x2 on the same coordinate plane.

• How are they the same? How are they different?

• Predict how the graph of y=1/3x2 will be similar and different to the graph of y=x2?

### Vocabulary:

• Standard Form of a Quadratic Function = a function that can be written in the form of ax2+bx+c where a does not equal 0.

• Quadratic Parent Function = f(x) = x2 or y = x2

• Parabola: U-shaped curve = the graph of a quadratic function

• Axis of Symmetry = The line that divides the parabola into 2 matching halves.

• Vertex = The highest or lowest point of a parabola

• Minimum/Maximum….

### Compare the widths of parabolas..

• The larger the a…..?

• The smaller the a….?

### Graph:

• Graph y=2x2 and y=2x2+3 and y=2x2-4 on a piece of graph paper.

• What conclusion can you make about ‘c’?

### More Rules:

• Review: X = is a vertical or horizontal line?

• Vertex of a parabola is the point…?

• Axis of symmetry divides the parabola in half at what point?

• Axis of symmetry of a quadratic function: x = -b/2a which is also the x-coordinate of the vertex.

### Graph y=ax2+bx+c

• Graph the function -3x2+6x+5.

• Step 1: Find the equation of the axis of symmetry and the coordinates of the vertex…

### Graphing continued…

• Axis of symmetry = -6/2(-3) = 1

• Plug in 1 for x and solve for the y-coordinate of the vertex.

### Graphing continued:

• Vertex = (1,8)

• Axis of symmetry = x=1

### Graphing Continued…

• Find 2 other points on the graph.

• 1. Use the y-intercept where x = 0.

• When x=0, y=5

• 2. Try another point on the same side of the vertex as the y-intercept… Let x = -1

• When x=-1, y=-4 so another point is (-1, -4)

### Graphing Continued…

• Step 3: Reflect the points (0,5) and (-1, -4) across the axis of symmetry to get 2 more points… Draw the parabola.

• Graph f(x) = x2-6x+9

### Recap: Conclusions

• y=a2+bx+c

• Positive a: opens up

• Vertex = minimum

• y=-a2+bx+c

• Negative a: Opens down

• Vertex = maximum

• The larger the a, the narrower the graph.