Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Algebra 2 Unit 9 Unit Test Good Luck ________________________ 28 January, 2005 Fischer Vertex Form: y – k = a(x – h)2 Vertex: x = -b ± b2 - 4ac x= 2a -b 2a Standard Form: y = ax2 + bx + c Roots (x-intercepts) Form: y = a(x - r)(x - s) 1. Given f x 3x2 6 x 4 a. What’s the vertex? [6] b. Does this parabola open up or down? [3] c. What’s the y-intercept? [3] d. Does this parabola have a maximum or a minimum? If so, where does it occur? [5] e. When is this function neither increasing or decreasing? [4] 2. Let f x 2 x2 13x 7 . Show all your work. a. Find f 8 and write your answer as an ordered pair. [5] b. Find x when f x 13 and write your answer as an ordered pair. [8] c. Find x when f x 35 and write your answer as an ordered pair. [8] 3. Find the particular equation of the quadratic function containing the given ordered pairs. Show all your work. a. The vertex is (4, 1) and includes the point (2, 9). [9] b. The roots (4, 0) and (-6, 0) that includes the point (3, 27). [9] 4. Use the discriminant to determine the type of roots the quadratic has: either (1) Rational, (2) Irrational, (3) Complex, or (4) One double root. Show all your work! a. y = x2 – 18x + 81 [5] b. y = -x2 – 10x – 12 [5] 5. The following quadratic has one x-intercept: y = 5x2 + 8x + c. Your job is to calculate the exact value of c. [5] 6. Given: y – 9 = 3(x – 2) 2. Answer the following questions. a. What is the vertex? [4] b. Find the y-intercept. [7] c. Make a sketch of the graph. [3] d. Based on your sketch and without doing any algebra on the given equation, determine what values the discriminant can be. [5] 7. Given y – 12 = -3(x + 2) 2, find the x-intercepts. [6] Bonus We have been studying quadratic equations; equations of the form Y = ax2 + bx + c. Below is the graph of a cubic equation, y = ax3 + bx2 + cx + d. Notice the cubic is raised to the third power, it has three roots! Many of the rules of quadratics apply to cubics, however, their graphs are very different pictures. Notice that one end goes up to positive infinity and one end goes down to negative infinity. 1. Draw a cubic equation that has one double root, and one single root with a > 0. 2. Draw a cubic with three roots and a < 0.