Solve:

2. (x+5)(x−5) ∙ Solve: B. A. 10x ∙ 2 ∙ (x+5) = 4 20 − 2x = 4 2 x + 10 = 4 2 x = −6 −2x = −16 x = 8 x = −3 Check: Check:

3. slope: y2− y1 m = x2 − x1 Where is the graph of each of these points located in the coordinate plane? A. (−2, 4) B. (1, 3) C. (0, 2) quadrant II quadrant I y-axis Find the slope of the line that passes through each pair of points. (x1,y1) (x2,y2) undefined • (1, −1) and (1, 3) • B. (−2, 3) and (2, 5) • C. (−1, 3) and ( 2, 3) (x1,y1) (x2,y2) (x1,y1) (x2,y2)

4. 4 + 2 x1 + x2 y1 + y2 5+ 7 ( ) ( ) 2 2 2 2 , , Find the slope and y-intercept of the line whose equation is: y = − y = mx + b y-intercept: b = 3 slope: m = − x + 3. Find the midpoint of the segment with endpoints (4, 5) and (2, 7). midpoint: = (3, 6) Find the slope of the line whose equation is: 3x + 6y = 2. y = mx + b slope: m = − 6y = − 3x + 2 y = −x + y = −x +

5. −5 = ∙ 8 + b 9 − 5 4 = m = slope: 6− 3 3 Find the equation of a line passing through the point y = mx + b (8, −5) with slope of . −5 = 6 + b y = x − 11 b = −11 Find the equation of the line that passes through the points (3, 5) and (6, 9) . y = mx + b 5 = ∙ 3 + b y = x + 1 5 = 4 + b 1 = b

6. • (1,−2) = Graph the equations: A. y = −5x + 3 • (0, 3) rise y = mx + b y-intercept: b = 3, run slope: m = −5 B. x = 2 C. y = 1

7. A. y = x − 1 B. 2y = x + 9 C. 3y − 6 = 9x D. y = − x − y = x + slope: − slope: slope: y = − x + slope: − Which equation has a graph that is a line parallel to the graph of x + 2y = 9 : 3y = 9x + 6 y = 3x + 2 slope: 3 x + 2y = 9 Parallel lines have the same slope. 2y = −x + 9 Answer: D

8. x y −3 0 3 Using a domain of {−3, 0, 3}, complete a table of (x,y) values for −2x +3y = 3 . −2(−3) + 3y = 3 −2 ∙ 0 + 3y = 3 −2 ∙ 3 + 3y = 3 −1 6 + 3y = 3 0 + 3y = 3 −6 + 3y = 3 1 3y = −3 3y = 3 3y = 9 3 y = −1 y = 1 y = 3 Find the domain and range for the function: {(−2, 1), (0, 2), (1, 4), (2, 5)} domain: {−2, 0, 1, 2} range: {1, 2, 4, 5} Describe the graph of y = −2x2 + 1. A parabola that opens downward with a y-intersection point of (0,1)

9. Find the vertex point for the function: f(x) = x2 +4x − 2. f(x) = ax2 + bx + c vertex: y = x2 + 4x − 2 y = (−2)2 + 4(−2) + (−2) y = 4 + −8 + (−2) vertex point: (−2, −6) y = −6 Describe the solution of this system of equations: −3x + y = −1 3x − y = 5 −3x + y = −1 3x − y = 5 Parallel lines have the same slope. y = 3x − 1 −y = −3x + 5 slope: 3 y = 3x − 5 slope: 3 No solution, because the line graphs of the equations are parallel.

10. Write a system of equations that could be used to solve this problem: The math club sold 200 raffle tickets for a total of $110 at $.50 for students and $.75 for adults. x + y = 200 Let: x = num. of student tickets sold y = num. of adult tickets sold .50x + .75y = 110 Write a system of equations that could be used to solve this problem: Joe is 28 years older than his daughter Mary. In 12 years he will be three time as old as Mary is now. y = x + 28 Let: x = Mary’s age y + 12 = 3x y = Joe’s age

11. x = x = Solve each system: 4x − y = −1 • 4x − y = −1 • 6x + 5y = 18 ( ) ∙ 5 20x − 5y = −5 4 ∙ − y = −1 6x + 5y = 18 2 − y = −1 26x = 13 3 = y Sol. ( , 3 ) • x + 7 = −9y • y = 7 − 4x substitute y = 7 − 4x x + 7 = −9 (7 − 4x) y = 7 − 4 ∙ 2 x + 7 = −63 + 36x y = 7 − 8 70 = 35x Sol. ( 2 ,−1 ) y = −1 2 = x

12. x + y = −1 x + y = −1 y = x − 1 x y How are the graphs of the two equations in this system related? −2x + y = 1 −2x + y = 1 y = 2 x + 1 • y-intercept: (0, 1) • -rise slope: • -run • The lines are perpendicular because the slopes are negative reciprocals. y-int.: (0, −1) -rise slope: -run

13. The radius r of a circle varies directly as the circumference c. If the circumference is 3p when the radius is 5, find the radius when the circumference is 8p. ∙ 8p r = k ∙ c r = k ∙ c 5 = k ∙ 3p Solve the proportion: x ∙ (x − 2) = 1 ∙ 3 x2 − 2x = 3 x2 − 2x − 3 = 0 (x + 1)(x − 3) = 0 x + 1 = 0 or x − 3 = 0 x = −1 x = 3 sol. set: {3, −1}

14. -4 -3 -2 -1 0 1 2 3 4 -2 -1 0 1 2 3 4 5 6 -4 -3 -2 -1 0 1 2 3 4 -4 -3 -2 -1 0 1 2 3 4 Solve each inequality and graph the solution set on a number line. B. 2 − 5x < 7 A. 7x + 1 ≤ 22 −5x < 5 7x ≤ 21 x > −1 x ≤ 3 C. 2(4x −2) ≥ 3(2x + 2) D. −3 ≤ 2x − 1< 5 8x − 4 ≥ 6x + 6 −2 ≤ 2x < 6 2 x ≥ 10 −1 ≤ x < 3 x ≥ 5

15. -4 -3 -2 -1 0 1 2 3 4 Solve: −3 ≤ 2x + 1 ≤ 3 x − 2 = 10 or x − 2 = −10 −4 ≤ 2x ≤ 2 x = 12 or x = −8 −2 ≤ x ≤ 1 sol. set: {12, −8} no solution: Ø *Absolute value of an expression cannot equal a negative num.

16. √ √ A. Jerry wants to rent a car for his trip. The rental cost $75 a week plus $.20 a mile. Write an inequality that can be used to find the most number of miles Jerry can travel if he wants to spend a maximum of $300. Let n = number of miles Jerry can travel. 75 + .20n ≤ 300 B. The top of a ladder is propped against the side of a house 12 feet from the ground and the bottom of the ladder is 5 feet from the wall. How tall is the ladder? a2 + b2 = c2 52 + 122 = c2 c= ? 25 + 144 = c2 b= 12 ft 169 = c2 a= 13 = c 5 ft The ladder is 13 ft tall.

17. Simplify:

18. √ √ Solve: C. (x + 4)2 = 16 x + 4 = ±4 x − 1 = 100 x + 4 = 4 or x + 4 = −4 x = 101 x = 0 or x = −8 D. 6n2 − 150 = 0 6n2 = 150 n2 = 25 n = 5, −5 3x + 1 = 100 3x = 99 x = 33

19. Simplify: Use: F.O.I.L F-first x first O-outside x outside I-inside x inside L-last x last

20. Solve using the quadratic formula: ax2 +bx + c = 0 x2 −3x −7 = 0 a = 1, b = −3, and c = −7

21. Use the discriminant to find the number of real number roots of this equation: ax2 +bx + c = 0 Discriminant: b2 − 4ac 5x2 +10x + 5 = 0 = 102 − 4∙5∙5 a = 5, b = 10, and c = 5 = 100 − 100 = 0 The discriminant is equal to “0” so there is one real number root.