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Quadratic Graphing and Concavity

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Quadratic Graphing and Concavity

Part 1: Understanding Quadratic Graphs

Choose the best answer for each question.

1. What shape does the graph of a quadratic equation usually have?

A straight line

A parabola

A circle

2. A parabola with a positive coefficient of x² is:

Concave up

Concave down

Neither

3. A parabola with a negative coefficient of x² has:

A minimum point

A maximum point

No turning point

Part 2: Complete the Table and Graph

For each equation, complete the table for x = −2, −1, 0, 1, 2. Plot the points, draw a smooth parabola and state whether the graph is concave up or concave down.

4. y = x²

x:   −2     −1     0     1     2

y:   ______    ______    ______    ______    ______

Concavity: ______________________________

5. y = x² + 1

x:   −2     −1     0     1     2

y:   ______    ______    ______    ______    ______

Concavity: ______________________________

6. y = −x²

x:   −2     −1     0     1     2

y:   ______    ______    ______    ______    ______

Concavity: ______________________________

7. y = −x² + 2

x:   −2     −1     0     1     2

y:   ______    ______    ______    ______    ______

Concavity: ______________________________

8. In one sentence, explain how the sign of the x² coefficient tells you the concavity of a quadratic graph.

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