quadratic equation

Practic problems

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NAME _____________________________________________ DATE _____________________________ PERIOD _____________ Chapter 4 14 Glencoe Algebra 2 4-2 Practice Solving Quadratic Equations By Graphing Use the related graph of each equation to determine its solutions. 1. ?3?2 + 3 = 0 2. 3?2 + ? + 3 = 0 3. ?2 ? 3? + 2 = 0 Solve each equation. If exact roots cannot be found, state the consecutive integers between which the roots are located. 4. ?2?2 ? 6? + 5 = 0 5. ?2 + 10? + 24 = 0 6. 2?2 ? ? ? 6 = 0 7. ??2 + ? + 6 = 0 8. ??2 + 5? ? 8 = 0 9. GRAVITY Use the formula h(t) = ?0? ? 16? 2, where h(t) is the height of an object in feet, ?0 is the object?s initial

Practice worksheet

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Algebra

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NAME DATE PERIOD NAME DATE PERIOD NAME DATE PERIOD 4-2 Practice Solving Quadratic Equations By Graphing Use the related graph of each equation to determine its solutions. 1. 2. 3. Solve each equation. If exact roots cannot be found, state the consecutive integers between which the roots are located. 4. 5. 6. 7. 8. 9. GRAVITY Use the formula h(t) = , where h(t) is the height of an object in feet, is the object?s initial velocity in feet per second, and t is the time in seconds. a. Marta throws a baseball with an initial upward velocity of 60 feet per second. Ignoring Marta?s height, how long after she releases the ball will it hit the ground?

alg2 review

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Algebra

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Curves

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Tangent

quadratic equation

Linear differential equation

H/GT Algebra II - Semester Exam Final Review 1.) Solve 4 264 16 1 0b b? ? ? 2.) What is the vertex of 23 24 5y x x? ? ?? 3.) Graph 22( 1) 1y x? ? ? 4.) Solve 25 19 4n n? ? 5.) Write an equation of a parabola that passes through the points (0, 2), (-2, 6), and (6, 14). 6.) Write the equation for the graph below. 7.) Write an equation of a parabola (general form) with vertex (0, 0) and directrix y = 2. 8.) Find the vertex of 24 4x y y? ? 9.) Graph 2 3y x? ? 10.) Write an equation of a circle with center (4, -3) and radius 5. (General form) 11.) Find the center and radius: 2 2 8 4 12 0x y x y? ? ? ? ?

AHSME 1991

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USA AIME 1991 1 Find x2 + y2 if x and y are positive integers such that xy + x+ y = 71x2y + xy2= 880. (0) Rectangle ABCD has sides AB of length 4 and CB of length 3. Divide AB into 168 congruent segments with points A = P0, P1, . . . , P168 = B, and divide CB into 168 congruent segments with points C = Q0, Q1, . . . , Q168 = B. For 1 ? k ? 167, draw the segments PkQk. Repeat this construction on the sides AD and CD, and then draw the diagonal AC. Find the sum of the lengths of the 335 parallel segments drawn. Expanding (1 + 0.2)1000 by the binomial theorem and doing no further manipulation gives ( 1000 0 ) (0.2)0 + ( 1000 1 ) (0.2)1 + ( 1000 2 ) (0.2)2 + ? ? ?+ ( 1000 1000 ) (0.2)1000 = A0 +A1 +A2 + ? ? ?+A1000, (0) where Ak = (1000 k )