# Factor and graph

Final Quiz Math 25 Spring 2021 Name ______________________ (5 pts) 1. Find the slope-intercept form of the equation of the line that passes through (1 , 4) ππππππ (5 , β4) (6 pts) 2. Graph ππ(π₯π₯) = 2π₯π₯ 2 β 12π₯π₯ + 13, labeling the vertex and 2 other points, using symmetry. (8 pts) 3. Factor and graph ππ(π₯π₯) = 2π₯π₯ 3 + 9π₯π₯ 2 β 6π₯π₯ β 40, labeling all intercepts. (8 pts) 4. Graph the following rational function (label all intercepts and asymptotes) ππ(π₯π₯) = 2π₯π₯β5 π₯π₯+1 (6 pts) 5. Solve the following exponential equation. Give the exact answer and an approximation to two decimal places. 73π₯π₯β5 + 9 = 23 (8 pts) 6. Complete the square and graph the following conic section, labeling 5 points. π₯π₯ 2 β 6π₯π₯ + 2π¦π¦ 2 β 8π¦π¦ + 1 = 0 (8 pts) 7. Solve the following system using a matrix and converting the matrix to reduced row echelon form, without introducing any fractions. 3π₯π₯ β 2π¦π¦ + 5π§π§ = β7 π₯π₯ β π¦π¦ + 3π§π§ = β5 4π₯π₯ + π¦π¦ + 6π§π§ = 6 8. Consider the sequence 17, 13, 9, 5, β¦ (3 pts) a. What is the general term of this sequence? (3 pts) b. What is the 127th term in this sequence? (3 pts) c. What is the sum of the first 127 terms in this sequence? 9. Consider the sequence 2, 8, 32, β¦ (3 pts) a. What is the general term of this sequence? (3 pts) b. What is the 13th term in this sequence? 10. Find the following finite sums. (5 pts) a. 2 + 4 + 8 + 16 + β― + 8192 = (5 pts) b. 9 + 13 + 17 + 21 + β― + 761 = (4 pts) 11. Find the following infinite sum. 2 2 2 2 + 3 + 9 + 27 + β― (6 pts) 12. Suppose you have an arithmetic sequence where the 10th term is 21 and the 29th term is 78, find the general term for the sequence. (6 pts) 13. Write out the first five terms of the binomial expansion below: (π₯π₯ β 2π¦π¦)16

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