Quadratic and Polynomial Functions

In this Practice set, you will solve problems related to quadratic functions. You will need to know the following: • Standard form: y = ax ^{2} + bx + c• Axis of Symmetry: Equation of the form x = ...• Vertex (x, ,y) where x = -b/2a• Vertex is a max or min• Parabola opens up or down• Roots = zeros or x-intercepts• Vertex Form: y = a(x – h) ^{2} + kConvert the Quadratic to Vertex Form, Does the parabola open up or down? Is the vertex a maximum or minimum? Identify the Vertex, Line of Symmetry, and any zeros. up down opens: Vertex Form: max/min? f(x) = x^{2} – 8x + 16f(x) = (x – )^{2} + ( , ) vertex line of symmetry x = ( , 0) zero Convert the Quadratic to Vertex Form, Does the parabola open up or down? Is the vertex a maximum or minimum? Identify the Vertex, Line of Symmetry, and any zeros. opens: up/down Vertex Form: max/min? f(x) = -x^{2} – 4x + 1f(x) = (x – )^{2} + ( , ) vertex line of symmetry x = 2 irrational 2 complex 2 rational 1 rational zeros Convert the Quadratic to Vertex Form, Does the parabola open up or down? Is the vertex a maximum or minimum? Identify the Vertex, Line of Symmetry, and any zeros. opens: up/down Vertex Form: max/min? f(x) = -2x^{2} + 16x + 31f(x) = (x – )^{2} + ( , ) vertex line of symmetry x = 2 irrational 2 complex 2 rational 1 rational zeros Write two equations of parabolas with the x-intercepts shown: one that opens up, f(x), and one that opens down, g(x). Opens down: Opens up:f(x) = x ^{2} + x + g(x) = x ^{2} + x + (4, 0) and (8, 0)-1 ? 1 ? -12 ? 12 ? 32 ? -32 ? Opens down: Opens up:Write two equations of parabolas with the x-intercepts shown: one that opens up, f(x), and one that opens down, g(x). g(x) = -1x ^{2} - x + f(x) = 1(x – )(x + ) (-3, 0) and (½, 0)Describe the end behavior of the polynomial function. Note: Type the word "down" or "up" into each box.Left end:f(x) = 6 – 2x + 4x^{2} – 5x^{3}Right end: Describe the end behavior of the polynomial function. Note: Type the word "down" or "up" into each box.Left end:f(x) = 1 – x^{6} Right end: Describe the end behavior of the polynomial function. Note: Type the word "down" or "up" into each box.Left end:f(x) = 4x^{5} – 7xRight end: Describe the end behavior of the polynomial function. Note: Type the word "down" or "up" into each box.Left end:f(x) = ¼(3x^{4} – 2x + 5)Right end: |

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