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CHAPTER 1 TEST REVIEW #4 pg 5 What is the length and midpoint of line “CD”? Coordinates: C(-2,-1); D(4,9) A) Length: a) Use the distance formula: b) Insert the points c) Calculate = d) Simplify = X = #4 pg 5, cont. What is the length and midpoint of line “CD”? Coordinates: C(-2,-1); D(4,9) B) Midpoint: a) Use the midpoint formula: b) Insert the points c) Calculate d) Simplify (1,4) Example pg.2 Solve the equations simultaneously to find the intersection point. Graph and label the intersection point. A) Solve the equations: 2x + 5y = 10, and 3x + 4y = 12 a) Multiply in order to make a common factor (x3) (x2) 2x + 5y = 10 3x + 4y = 12 = = 6x + 15y = 30 6x + 8y = 24 b) Now subtract the bottom equation from the top to yield: 7y = 6 c) Divide both sides by 7: y = 6/7 d) Plug y back in to solve for x: 2x + 5(6/7) = 10 x = 20/7 #9 pg.5 Given: 3x - ay = 15, find a if (9, 6) lies on this line. A) Plug in x and y. 3(9) - a(6) = 15 B) Solve for a. a = 2. #13 pg.11 Find the slope and the y intercept of the following equation: 4x – 2y = 8 a) Rearrange the equation into the slope intercept form. b) subtract 4x: -2y = -4x + 8 c) divide by -2: y = 2x – 4 d) the slope is 2, the y intercept is -4 #18 pg.11 Which of the following equations have parallel lines and which have perpendicular? a) 3y = 5x - 5 b) y = -3x/5 +4 c) 10y = -6x -7 d) parallel lines: b and c, perpendicular lines: a and b, a and c, #6 pg.16 Write the equation of the line that passes through the points (0,5) and (6,1). a) First you must find the slope, using the slope equation b) Plugging in your numbers you get the slope to be 2/3 c) Plug in one of the points into the equation y = mx + b to find the y intercept d) 1 = (-2/3) (6) + b, b = 5 e) The equation: y = -2x/3 + 5 #13 Find the equation of the line that passes through the point (8, -2) and is perpendicular to the line y =-2x + 7 a) The slope is the negative reciprocal of -2, so it is ½. b) Plug in the point to solve for b. c) -2 = (1/2) (8) + b, b = -6. d) The equation is y = x/2 – 6 #5 Find the equation of the line that passes through the points (8, 3) and (2, -1) a) Using the slope formula, we get the slope to be 2/3 b) Now plug in a point to solve for b c) 3 = (2/3) (8) + b, b = -7/3 d) The equation is y = 2x/3 – 7/3 #4 Find the equation of the line that has an x intercept of -1 and a y intercept of 6. a) Since these are our intercepts, we know our two points are (-1, 0) and (0, 6). b) Once again, using the slope formula, the slope is 6. c) Plug in one of your points: 6 = 6(0) + b, b = 6. d) The equation is y = 6x + 6 #7 Find the equation of the horizontal line that passes through the point (5, -7) a) This is a horizontal line, meaning it has a slope of 0 b) Every y coordinate on this line will be -7, so that is also the y intercept. c) The equation is y = -7. #12 Find the equation of the line that passes through the point (-2, 4) and parallel to the line that passes through the points (1, 1) and (5, 7) a) First we must find the slope of the line through (1, 1) and (5, 7) using the slope equation b) This gives us a slope of 3/2, now plug in (-2, 4) to solve for b. c) 4 = (3/2) (-2) + b, b = 7 d) The equation is y = 3x/2 + 7 #16 pg. 23 A recording studio invests $24,000 to produce a master tape of a singing group. It costs $1.50 to make each copy of the master and cover the operating costs a) Express the cost of producing t tapes as a function C(t). b) C(t) = 1.5t + 24,000 c) If each tape is sold for $6.50, express the revenue (the total amount received from the sale) as a function R(t). d) R(t) = 6.5t #2 pg. 28 Simplify: √-49 - √-9 + √-36) a) 7i – 3i + 6i = 10i #4 pg. 28 Simplify: √-2 x √-5 a) - √10 #11 pg. 28 Simplify (6-i)(6+i) a) Using FOIL method, you get 36 + 6i -6i – i2 b i2 = -1, so the answer is 37 #21 pg. 28 Simplify (5+i)/(5-i) a) answer: 12/13 + 5i/13 Solve for x or y: a) (2x – 1)2 = -4 b) Take the square root of both sides: 2x – 1 = (+ or -) 2i c) Add one: 2x = 1 (+ or -) 2i d) Divide by two: x = ½ (+ or -) i e) y2 – 8y = 2 f) y = 4 (+ or –) 3 √2 y= 4 3 Example 1 pg. 38 Sketch the parabola y=2x2 -8x + 5. Label the x intercepts, the axis of symmetry, and vertex. a) Find the intersection points with the line y = 2x + 5 b) Answer: (0,5) y= 4 3 Finding a Quadratic Equation C(x) = ax2 + bx + c a) Given that C(12)= 152, C(22)=105, and C(30) = 165, set up the three equations to solve for a, b, and c 152 = a(12²) + b(12) + c y= 4 3 105 = a(22²) + b(22) + c 165 = a(30²) + b(30) + c Solve the equations simultaneously to find the quadratic equation.