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Quadratic Graphs and Values
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Quadratic Graphs and Values
Use each rule to calculate the y-values. For the graphing task, draw a set of axes in the space provided, then plot the points from all four tables on the same axes, draw smooth curves and label each vertex.
1.A quadratic curve opens downwards. Is its vertex a minimum or a maximum?
- A minimum
- A maximum
- It has no vertex
2.For Quadratic A, use y = (x − 3)² − 2 to complete the values: when x = 0, y = __; when x = 1, y = __; when x = 3, y = __; when x = 5, y = __.
3.For Quadratic B, use y = −(x − 3)² + 6 to complete the values: when x = 1, y = __; when x = 3, y = __; when x = 4, y = __; when x = 6, y = __.
4.For Quadratic C, use y = (x + 3)² − 2 to complete the values: when x = −5, y = __; when x = −3, y = __; when x = −1, y = __; when x = 0, y = __.
5.For Quadratic D, use y = −(x + 3)² + 6 to complete the values: when x = −6, y = __; when x = −4, y = __; when x = −3, y = __; when x = −1, y = __.
6.In the space below, draw a set of axes. Plot all points from Quadratics A, B, C and D on the same axes. Sketch each curve smoothly and label its vertex A, B, C or D.
7.State the vertex coordinates for each rule: A: y = (x − 3)² − 2; B: y = −(x − 3)² + 6; C: y = (x + 3)² − 2; D: y = −(x + 3)² + 6.
8.Compare the four rules and their curves. What reflection symmetry do they have, and how can you see it in the equations?
9.Change Quadratic A to y = 2(x − 3)² − 2. Describe how its curve differs from the original y = (x − 3)² − 2, then sketch the new curve.
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