advertisement

Name:_________________________________ Review: Sections 2.1-2.5 STANDARD FORM of a Quadratic: ______________________________ Vertex: ( , Finding zeros: ) Axis of symmetry: ______ (MEMORIZE) x-intercepts: zeros/roots/solutions Degree 2: In standard form: Set f(x) to zero and solve by using square roots (Remember ±) Not in standard form: factor and solve for x. If you cannot factor, use quadratic formula! (memorize) Higher than degree 2: Set f(x) to zero and try to factor by GCF or grouping. If it cannot factor, must use rational zero test. GRAPH THE FOLLOWING. 1) y =2(x + 1)2 - 4 Vertex:_________ Axis of Symmetry: ___________ x-intercept(s): _______________ 2) y = x2 – 6x + 7 (Get into standard form!) Standard Form: ___________________ Vertex:_________ Axis of Symmetry: ___________ x-intercept(s): _______________ 3) Write an equation in standard form that has a vertex (3, 6) and goes through the point (1, -2). 4) The path of a diver is given by the equation y= -2x2 + 20x – 46 where y is the height (in feet) and x is the horizontal distance from the end of the diving board. What is the maximum height of the diver? Write the following in standard form and identify the vertex. (Hint What process should you do!?) 5) y = x2 + 12x – 39 6) y = 3x2 + 24x + 49 7) y = -2x2 + 4x + 3 f(x) = ___________________ f(x) = ___________________ f(x) = ___________________ Vertex:_________ Vertex:_________ Vertex:_________ GRAPH THE FOLLOWING POLYNOMIALS BY HAND. 9) f(x) = 2x3 – 2x2 – 12x 8) f(x) = - x4 + 9x2 Zeros:________ Zeros:________ y-int:_________ y-int:_________ FIND THE ZEROS. Do NOT use completing the square. 10) f(x) = 2x3 + x2 – 72x – 36 11) f(x) = x2 – 4x + 5 12) Use the chart to determine where there is/are a root(s) ______________________________________________________ x -2 y -4 -1 2 0 1 3 5 2 -2 3 -1 WRITE AN EQUATION WITH THE GIVEN ROOTS. 13) 0 (double root), -7, 7 14) 3i, -6, 2 WRITE THE EQUATION OF EACH GRAPH. Answer:______________________________ Answer:_______________________________ 15) 16) COMPLETE THE FOLLOWING. SHOW ALL WORK! 17) Use the Remainder Theorem to determine if (x – 3) is a factor of (2x4 + 9x3 – 9x2 – 46x + 24)? 17. YES or NO 18) Is –2 a root of x4 + 5x2 – 36? Support! 18. YES or NO 19) Divide (x4 + x3 – 2x2 + 4x – 24) by (x – 2) and name the remaining polynomial 19. __________________ 20) Find the value of k so that the remainder is 0. (3x3 + 6x2 – kx – 9) ÷ (x + 3) 20. k = ______________ 21. y = x3 – 2x2 - 4x + 8 number of complex roots: number of possible positive roots: number of possible negative roots: Is –1 a root? Is 1 a root? possible roots: factors of factors of Zeros:_____________ y-int:_______ 22. y = 4x4 – 12x3 + 3x2 + 13x – 6 number of possible positive roots: number of complex roots: number of possible negative roots: Is –1 a root? Is 1 a root? possible roots: factors of factors of Zeros:_____________ y-int:_______ 23) The path of a football is represented by the equation y = -(x – 2)2 + 10 where x represents time in seconds and y represents the position in feet. a) After how many seconds has the football reached its maximum height? b) What is the maximum height? c) At what position does the object begin its path?