|
In this Practice set, you will solve problems related to quadratic functions. You will need to know the following: • Standard form: y = ax2 + 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 + k 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. up down opens: Vertex Form: max/min? f(x) = x2 – 8x + 16 f(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) = -x2 – 4x + 1 f(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) = -2x2 + 16x + 31 f(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) = x2 + x + g(x) = x2 + 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) = -1x2 - 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 + 4x2 – 5x3 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 – x6 Right end: Describe the end behavior of the polynomial function. Note: Type the word "down" or "up" into each box. Left end: f(x) = 4x5 – 7x Right end: Describe the end behavior of the polynomial function. Note: Type the word "down" or "up" into each box. Left end: f(x) = ¼(3x4 – 2x + 5) Right end: |