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College Algebra Unit 2 Take Home Quiz Due: Odd Classes October 13th Even Classes October 14th Name Directions: Show all work and reasoning to receive full credit. 1) Using the Pythagorean Theorem, determine whether or not the points are the vertices of a right triangle: (-9, 7), (-3, 7), (-3, 15). 2) Determine the center (h, k) and radius r of the circle 4 x2 4 y 2 12 x 16 y 5 0 . Graph the function. 1 1 3) Determine the general form of the equation of the circle with endpoints of a diameter at (6, -2) and (-4, 4). For Questions 4 & 5, determine an equation, in slope-intercept form, for the line with the given properties. 4) Parallel to the line 4 x 3 y 3 ; 5) Perpendicular to the line 2 x 9 y 66 ; containing the point (6, 0). containing the point (6, -13). 6) Determine the equation, in general form, of the line in the graph illustrated below. 10 8 6 (5,5) 4 (5,1) 2 -10 -8 -6 -4 -2 2 4 6 8 10 -2 -4 -6 -8 -10 For Questions 7 & 8, determine the domain of the functions. Answers should be in interval notation. x4 7) h( x) 3 8) g ( x) 3 7 x x 4x 9) Determine and simplify the difference quotient f, f ( x h) f ( x ) , h 0 , given f ( x) 2 x2 9 x 5 . h 10) Answer the following questions about the function f (x) 3x 6 x2 4 5 a) If f (x) , what is x? What point(s) are on the graph? 3 b) List the x-intercepts and y-intercept, if any, of the graph of f. 11) Answer the following questions about the given functions, 𝑓(𝑥) = 2𝑥 + 2 and 𝑔(𝑥) = 2𝑥 2 − 2. a) f + g b) f – g c) 𝑓 ∙ 𝑔 d) 𝑓 𝑔 e) f(x + 3) 12) Write an equation in general form for the circle with a radius = √7 and center = (3, -4). 13) Find all points (x, y) with the y coordinate of -3 that are 3√5 units from (5, 2). 14) Determine the other endpoint of a segment whose midpoint is (4, -2) and has one endpoint at (-7, 3).