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MATH 107 Mathematics Equations & Functions Solved Quiz 2

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Name: ____________________ Date: _____________________ MATH 107 Quiz 2 1) Find the distance d between the points and the midpoint M of the line segment which connects them. (5, 7) and (12, 14) √(x − x ) + (y − y ) D = √(5 − 12) + (7 − 14) D = √(− 7) + (− 7) D= 2 1 2 2 1 2 2 2 2 x1 +x2 y 1 +y 2 2 , 2 ) ( 5+12 , 7+14 ) 2 2 ( 17 , 21 ) 2 2 M =( M= M= 2 D = √98 = 7√2 2) For the equation y = x2 + 6x + 5 : a. Find the x- and y-intercept(s) of the graph, if any exist. b. Create a table of sample points on the graph of the equation. ​ c. Plot the sample points and create a rough sketch of the graph of the equation. ​ d. Test for symmetry. If the equation appears to fail any of the symmetry tests, find a point on the graph of the equation whose reflection fails to be on the graph. a) y − int : S et x = 0 y = 02 + 6(0) + 5 = 5 y − int = (0, 5) x − int : S et y = 0 0 = x2 + 6x + 5, solve f or x (x + 5)(x + 1) = 0, f actor x + 5 = 0 or x + 1 = 0, zero product rule x =− 5 or x =− 1 x − int = (− 1, 0) and (− 5, 0) b) x y=x^2+6x+5 -9 32 -7 12 -5 0 -3 -4 -1 0 0 5 1 12 3 32 5 60 c) Desmos online calculator.(​https://www.desmos.com/calculator​ ) d) The graph is not symmetric about the x-axis. (1, 12) is on the graph but (-1, 12) is not. The graph is not symmetric about the y-axis. (-5, 0) is on the graph but (5, 0) is not. The graph is not symmetric about the origin. (1,12) is on the graph but (-1, -12) is not ...
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