C. Mind Your p's and q's
Completion requirements
C. Mind Your p's and q's
In Section C, you are going to look at characteristics of quadratic functions that depend on the values of \(p\) and \(q\).
| Investigation |
Effect of \(p\) and \(q\)
Using your graphing calculator, or another graphing program, such as Desmos, graph the following functions. Compare the other functions to the basic quadratic function, \(f(x) = x^2 \). Use the table below to investigate the effects of \(p\) and \(q\) on the function.
Look over the table, and think about any conclusions you could make regarding the values of \(p\) and \(q\) with respect to the vertex and the equation of the axis of symmetry.
| Functions | |||||
|---|---|---|---|---|---|
\(f(x) = x^2 \), \(g(x) = (x - 1)^2 \), \(h(x) = (x + 1)^2 \)
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Value of \(p\)
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Value of \(q\)
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Vertex | Equation of the Axis of Symmetry
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| \(f(x) = x^2 \) | |||||
| \(g(x) = (x - 1)^2 \) | |||||
| \(h(x) = (x + 1)^2 \) | |||||
| Functions |
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|---|---|---|---|---|---|
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\(f(x) = x^2 \), \(g(x) = x^2 - 2 \), \(h(x) = x^2 + 2 \)
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Value of \(p\)
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Value of \(q\)
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Vertex | Equation of the Axis of Symmetry
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| \(f(x) = x^2 \) |
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| \(g(x) = x^2 - 2 \) |
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| \(h(x) = x^2 + 2 \) |
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| Functions |
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|---|---|---|---|---|---|
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\(f(x) = x^2 \), \(g(x) = (x - 1)^2 - 2 \), \(h(x) = (x + 1)^2 - 2\)
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Value of \(p\)
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Value of \(q\)
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Vertex | Equation of the Axis of Symmetry
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| \(f(x) = x^2 \) |
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| \(g(x) = (x - 1)^2 - 2\) |
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| \(h(x) = (x + 1)^2 - 2\) |
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| Functions |
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|---|---|---|---|---|---|
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\(f(x) = x^2 \), \(g(x) = (x - 1)^2 + 2\), \(h(x) = (x + 1)^2 + 2\)
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Value of \(p\)
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Value of \(q\)
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Vertex | Equation of the Axis of Symmetry
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| \(f(x) = x^2 \) |
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| \(g(x) = (x - 1)^2 + 2\) |
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| \(h(x) = (x + 1)^2 + 2\) |
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Look over the table, and think about any conclusions you could make regarding the values of \(p\) and \(q\) with respect to the vertex and the equation of the axis of symmetry.