advertisement

Chapter 1: Lesson Exercise Graph Quadratic Functions in Standard Forms What is the effect on the graph of the function y = x2 when it is changed to y = –2x2 + 3? Graph Quadratic Functions in Vertex or Intercept Form Write the quadratic function y = –2(x – 1)(x + 3) in standard form. Give the vertex, axis of symmetry, and xintercepts. Is the vertex a maximum or minimum point? Find the zeros of the function y = x2 + 10x – 24 by rewriting the function in intercept form. Explain what this tells you about the graph of the function. Solve x2 + bx + c = 0 by Factoring Solve ax2 + bx + c = 0 by Factoring A rectangular rug has an area of 15 square units. It measures 4x + 5 units long and x + 4 units wide. Find the value of x. Solve Quadratic Equations by Finding Square Roots Perform Operations with Complex Numbers Use the Quadratic Formula and the Discriminant Write the expression as a complex number in standard form. (2 – 5i)(–3 + 9i) KEY IDEAS/Essential Questions/Formulas/etc. Graph the function. Label the vertex and the axis of symmetry. 1. y = –2x2 2. g(x) = 3 2 9 x 3x 4 4 Find the zeros of the function by rewriting in intercept form. 9. f(x) = 2x2 – 4x 10. y = 2x2 – 11x – 21 11. Simplify 6• 12 • 6 • 2. Graph the function. Label the vertex and the axis of symmetry. For Exercise 5, also label the x–intercepts. 3. y = 1 (x + 1)2 – 2 2 Solve the equation. 12. 25x2 = 16 13. x2 – 3x + 5 = 0 4. y = –2(x – 1)(x – 2) 14. Write 1 3i as a complex number in standard form. 2 5i 15. Write (3 – 2i) – (–11 – 9i) as a complex number in standard form. 5. Tell whether y = –3(x + 1)2 + 4 has a minimum value or a maximum value. Then find that value. Factor the expression. 6. j2 – 3j – 10 7. –2x2 + 6x + 56 8. Solve –3u = u2. 16. Solve r2 = 18 – 7r. 17. Find the discriminant of 3p2 – 6p + 8 = 0 and give the number and type of solutions to the equation. Chapter 2: Lesson Exercise Use Properties of Exponents Simplify (5x3y–4)3. Tell which properties of exponents you used. Evaluate and Graph Polynomial Functions State the degree, type, and leading coefficient of the polynomial function: g(x) = 6x3 + 9x2 – 7. Then use direct substitution to evaluate the polynomial function for x = 3. Find the sum of 3x2 – 4x + 9 and 4x2 – 5 . Find the product of the polynomials 3x2 – 4x + 9 and 2x – 5. Add, Subtract, and Multiply Polynomials KEY IDEAS/Essential Questions/Formulas/etc. What are ALL the properties of exponents? Factor and Solve Polynomial Equations You must know ALL the ways to factor. Synthetic/Long Division Divide 2x2 – 7x + 9 by x – 2 using LONG division and SYNTHETIC division. Simplifying Radical Expressions Simplify: 80 x 3 y 8 z 9 What does it mean to rationalize the denominator? Simplify: 3 What is a conjugate? Simplify: Finding Factors and Solutions of Polynomials Using the Factor Theorem and Rational Zero Test 5 3 7 2 6 Find all of the real zeros of the polynomial How do factors and solutions relate? 2x – 4x + x – 20 4 2 What is the rational zero test? 1. Simplify (q2u4)–2. Factor the polynomial completely using any method. 6. 1 4 x –4 4 7. y3 + 6y2 – 3y – 18 2. Use direct substitution to evaluate –2x3 + 2x2 + 6x – 4 for x = –1. Divide using polynomial long division or synthetic division. 8. (x3 – 13x – 12) ÷ (x – 4) 3. Use synthetic substitution to evaluate 2x4 – 4x2 + x – 20 for x = 2. 9. (x3 + 6x2 – 9x – 54) ÷ (x – 3) 4. (y5 – 2y2 – y4) + (3y2 – y4) 5. (x2 – 2x + 4)(3 – x)2