MM1A1i: Understand that any equation in x can be interpreted as the equation f(x) = g(x), and interpret the solutions of the equation as the x-value(s) of the intersection point(s) of the graphs of y = f(x) and y = g(x). Use the graph to the right to find one of the -3 solutions to the quadratic equation 2 x2 – 7x + 10 = 0. 10 -7 No solution x = 3 The graph of f(x) = x2 – 2x + 2 is shown to the x = -1 left. Use the graph to find the solution(s), if any, x = -1 and x = 3 to the equation x2 – 2x + 2 = 5. MM1A2a: Simplify algebraic and numeric expressions involving square roots. Order the expressions from least to greatest: 85 Simplify 81a2b4 , 641/2, 100. 9ab 641/2, 100 , 85 9a2b4 100 , 85 , 641/2 9ab2 100, 641/2, 85 9ab 641/2, 85 , 100 MM1A2b: Perform operations with square roots. Find the product. Simplify the radical expression . MM1A2c: Add, subtract, multiply, and divide polynomials. Multiply (x – 6)(3x2 + 10x – 1) 3x3 + 10x2 – 60x + 6 3x3 + 10x2 – x 3x3 – 18x2 + 10x2 + 6 3x3 – 8x2 – 61x + 6 Simplify (3x3 + 2x2 + 10) + (3x3 + 2x2 + 10x) 6x3 + 4x2 + 20x 9x3 + 4x2 + 100x 6x3 + 4x2 + 10x + 10 9x3 + 4x2 + 10x +10 MM1A2d: Add, subtract, multiply, and divide rational expressions. Simplify and determine the domain: . Add and simplify: . Simplify the expression
MM1A1i: Understand that any equation in x can be interpreted as the equation f(x) = g(x), and interpret the solutions of the equation as the x-value(s) of the intersection point(s) of the graphs of y = f(x) and y = g(x). Use the graph to the right to find one of the solutions to the quadratic equation x2 – 7x + 10 = 0. -7 -3 2 10 The graph of f(x) = x2 – 2x + 2 is shown to the left. Use the graph to find the solution(s), if any, to the equation x2 – 2x + 2 = 5. No solution x = 3 x = -1 x = -1 and x = 3 MM1A2a: Simplify algebraic and numeric expressions involving square roots. Order the expressions from least to greatest: 85 , 641/2, 100. 641/2, 100 , 85 100 , 85 , 641/2 100, 641/2, 85 641/2, 85 , 100 Simplify 81a2b4 9ab 9a2b4 9ab2 9ab MM1A2b: Perform operations with square roots. Find the product. Simplify the radical expression . MM1A2c: Add, subtract, multiply, and divide polynomials. Multiply (x – 6)(3x2 + 10x – 1) 3x3 + 10x2 – x 3x3 – 8x2 – 61x + 6 3x3 + 10x2 – 60x + 6 3x3 – 18x2 + 10x2 + 6 Simplify (3x3 + 2x2 + 10) + (3x3 + 2x2 + 10x) 6x3 + 4x2 + 20x 6x3 + 4x2 + 10x + 10 9x3 + 4x2 + 100x 9x3 + 4x2 + 10x +10 MM1A2d: Add, subtract, multiply, and divide rational expressions. Simplify and determine the domain: . Add and simplify: . Simplify the expression
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