Chapter Test A For use after the chapter Quadratic Relations and Conic Sections
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1 Test A. Find the distance between the points (, ) and (, 7). What is the midpoint of the line segment joining the two points?. The vertices of a triangle are (, ), (, ), and (, ). Classif the triangle as scalene, isosceles, or equilateral.. Write an equation for the perpendicular bisector of the line segment joining the points (, ) and (, 5). Graph the equation. Identif the focus, directri, and ais of smmetr of the parabola Write the standard form of the equation of the parabola with focus at (0, ) and verte at (0, 0). Copright Houghton Mifflin Harcourt Publishing Compan. All rights reserved. Graph the equation. Identif the radius of the circle Write the standard form of the equation of the circle whose radius is 7 units and whose center is the origin Algebra
2 Test A continued 0. Graph the equation Identif the vertices, co-vertices, and foci of the ellipse. 0.. Write an equation of the ellipse with center at (0, 0), a verte at (0, ), and a co-verte at (, 0)... An elliptical sign is feet long and ft 6 feet wide. Using the -ais as the major ais, write the equation of this ellipse. 6 ft... Graph the equation Identif the vertices, foci, and asmptotes of the hperbola. Write an equation of the hperbola with foci (0, ) and (0, ) and vertices of (0, ) and (0, ). Write an equation of the circle with its center at (, ) and a radius of 6. Write an equation of the ellipse with vertices at (, 5) and (, ) and co-vertices at (0, ) and (, ). Identif the line(s) of smmetr for the conic section ( ) 5. Solve the sstem.. ( ) Copright Houghton Mifflin Harcourt Publishing Compan. All rights reserved. Algebra
3 Test B. Find the distance between the points (, ) and (, 4). What is the midpoint of the line segment joining the two points?. The vertices of a triangle are (, ), (5, ), and (, ). Classif the triangle as scalene, isosceles, or equilateral.. Write an equation for the perpendicular bisector of the line segment joining the points (, ) and (, 4). Graph the equation. Identif the focus, directri, and ais of smmetr of the parabola Copright Houghton Mifflin Harcourt Publishing Compan. All rights reserved. 6. Write the standard form of the equation of the parabola with focus at (, 0) and verte at (0, 0). Graph the equation. Identif the radius of the circle Write an equation of the line tangent to the circle 5 9 at the point (, 5) Algebra
4 Test B continued 0. Graph the equation 9 5 Identif the vertices, co-vertices, and foci of the ellipse. 0.. Write an equation of the ellipse with center at (0, 0), a focus at (, 0), and a verte at (4, 0).. You are drawing an elliptical ee for an art cm project. The ee should be centimeters long and centimeters wide. Using the -ais as the major ais, write an equation of this ellipse. cm.... Graph the equation Identif the vertices, foci, and asmptotes of the hperbola Write an equation of the hperbola with foci (, 0) and (, 0) and vertices of (, 0) and (, 0). Write an equation of the ellipse with vertices at (, 4) and (, ) and co-vertices at (, ) and (, ). 6. Identif the line(s) of smmetr for the conic section 4( ) 9( ) 5 6. Use the discriminant to classif the conic section 5 0. Solve the sstem Copright Houghton Mifflin Harcourt Publishing Compan. All rights reserved. 4 Algebra
5 Test C. Find the distance between the points (, ) and (5, ). What is the midpoint of the line segment joining the two points?. Write an equation for the perpendicular bisector of the line segment joining the points (, ) and (4, ).. A commuter airplane must make stops before reaching its final destination. From its origin, the plane flies 00 miles west to reach its first destination, and 400 miles north to reach its second destination. Finall, it flies 700 miles east to reach its final destination. What is the straight-line distance between its origin and its final destination?... Graph the equation. Identif the focus, directri, and ais of smmetr of the parabola Copright Houghton Mifflin Harcourt Publishing Compan. All rights reserved. 6. Write the standard form of the equation of the parabola with focus at (, 0) and verte at (0, 0). Graph the equation and identif the radius of the circle Write the standard form of the equation of the circle with radius Ï 6 and whose center is the origin. 9. Write an equation of the line tangent to the circle 5 5 at the point (, ) Algebra 5
6 Test C continued 0. A target in an archer competition measures centimeters in diameter. A contestant s first arrow lands 50 centimeters to the left of and 0 centimeters above the center of the bulls-ee. Did the arrow hit the target? cm 0... Graph the equation Identif the vertices, co-vertices, and foci of the ellipse.... Write an equation of the ellipse with center at (0, 0), a focus at (, 0), and a verte at (5, 0).. Graph the equation Identif the vertices, foci, and asmptotes of the hperbola. 4. Write an equation of the hperbola with foci (0, 4) and (0, 4) and vertices of (0, ) and (0, ). Write an equation of the parabola with verte at (, ) and directri 5 6. Write an equation of the circle with center at (4, ) and radius Identif the line(s) of smmetr for the conic section ( ) 5.. Classif the conic section Write its equation in standard form. Solve the sstem Copright Houghton Mifflin Harcourt Publishing Compan. All rights reserved. 6 Algebra
7 for Quadratic Relations and Conic Sections Quiz. distance: 4 Ï, midpoint: (5, 4). distance: Ï 0, midpoint: (, 6). distance: Ï 5, midpoint: 7, Ï 9 9. ; 6 9 ; vertices: (65, 0), foci: (6 Ï 4, 0), asmptotes: , ft 49 Quiz ( 4) ( ) ( 4) 5 0( ). circle; ( ) ( 4) 5 5; answers 0. es; 5 0 < Quiz. ; vertices: (66, 0), co-vertices: (0, 6), foci: (6 Ï, 0) ( ) ( ) hperbola; 5 ; 6 9 Copright Houghton Mifflin Harcourt Publishing Compan. All rights reserved.. 4 ; vertices: (0, 6), co-vertices: (64, 0), foci: (0, 64 Ï ) ; vertices: (0, 64), foci: (0, 6 Ï ), asmptotes: (, ), (, ), (, 6), (, ) ( ) ( 4) 6. (0, 4), (0, ) Test A. Ï 7, (.5, 5). isosceles. 5 ; focus: 0,, directri: 5, ais of smmetr: -ais ; focus:, 0, directri: 5, ais of smmetr: -ais Algebra A9
8 continued answers r 5 4 r ; vertices: (6, 0); co-vertices: (0, 6); foci: (6 Ï 5, 0) r 5 r ; vertices: (0, 66), co-vertices: (6, 0), foci: (0, 64 Ï ) ; vertices: (6, 0); foci: (6 Ï, 0); asmptotes: ; vertices: (0, 64), foci: (0, 6 Ï 5 ), asmptotes: ( ) ( ) 5 6 ( ) ( ) (, ), (, ) 9. (4, ), (, 4) Test B. Ï, (0, ). scalene ; focus: 0,, directri: 5, ais of smmetr: -ais ; focus: 5, 0 directri: 5 5 ais of smmetr: -ais 4 ( ) ( ) , 5 hperbola. 4 Ï, Ï, 4 Ï, Ï 9. 0 Ï 4 4, 0 Ï 4 4, 0 Ï 4 4, 0 Ï 4 4 Test C. Ï 5, (4, ) Ï mi ; focus: 0,, directri: 5, ais of smmetr: -ais ; focus:, 0, directri: 5, ais of smmetr: -ais Copright Houghton Mifflin Harcourt Publishing Compan. All rights reserved. A0 Algebra
9 continued Copright Houghton Mifflin Harcourt Publishing Compan. All rights reserved. ; r 5 Ï es. ; vertices: (66, 0), co-vertices: (0, 6), foci: (6 Ï, 0) ; vertices: (0, 6), foci: (0, 6 Ï 5 ), asmptotes: ( ) 5 ( ) 6. ( 4) ( ) parabola; 5 4 ( ) 9. (6 Ï, 7) 0. (, ), (, ) Standardized Test. D. C. D D B 6. D A. B 9. A 0. D. C. C. C D mi; 5 5 ; ( ) ( 0) 5 50 a..7 in. b..7 5 or SAT/ACT Test. D. B. E A B 6. C E. D 9. A 0. C. B. E. E C C 6. 7 or. Alternative Assessment. a d. Complete answers should include: values for A, B, and C such that the discriminant (B 4AC) is negative for the circle (A 5 C) and the ellipse (A Þ C), is equal to zero for the parabola, and is positive for the hperbola. B must be equal to zero to ensure horizontal or vertical aes.; a standard form equation for each conic, obtained b completing the square; identification of (h, k) for each conic and a description of each resulting translation.. a. 5; See graph below. b. See graph below. c. (, 4); This point represents the second intersection of the circle and the bottom branch of the hperbola. d. See graph below. e. parabolic; B 4AC 5 0 4(0)() 5 0 f. (, 4) g. 5 4 ; See graph below. h. 4 mi; underestimates; Sample answer: The straight-line distance from the intersection of Main St and Carson Rd to the intersection of Carson Rd and Eagle Dr is shorter than the curved path traveled on Carson Rd. Similarl, the curved path followed on Eagle Dr is longer than the straight-line distance from the intersection of Carson Rd and Eagle Dr to the intersection of Eagle Dr and Main St. Post Office Main Street Eagle Drive Carson Road answers Algebra A
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