MPM 2D1 Unit 5 Summative Task - Quadratic Equations Name:. 50 Show your work for all questions. Remember to include units where appropriate. 1. Write the quadratic relation y = 4x + 40x - 15 in vertex form by completing the square. Show your work. [5 marks] 2. Solve the following equations by factoring. a) 5x2 - 2x = 0 [4 marks] b) x2 - 100 = 0 [4 marks] c) 5x2 + 11x + 2 = 0 [4 marks]3. Solve the quadratic equation 6x2 - 5x - 2 = 0 using the quadratic formula. Show your work. Round to two decimals. [4 marks] 4. When solving a quadratic equation there can be two unique solutions, one solution or no solutions. Complete the table below by drawing a sketch for each of these situations and stating the value or restriction for the discriminant. [6 marks] Number of Two unique solutions One solution No solution Solutions Sketch Value of the Discriminant b' - 4ac 5. Use the discriminant to determine the number of roots to the quadratic equation 5x2 + x +9 =0. Explain your answer. [3 marks] 26. Create equations of quadratics in standard form to satisfy each of the following. [3 marks] a) Contains 2 roots: b) Contains 1 root: c) Contains NO roots: 7. April sells specialty teddy bears at various summer festivals. Her profit for a week, P, in dollars, can be modelled by P = -0.1n' + 30n - 1200, where n is the number of teddy bears she sells during the week. a) If she sells 20 teddy bears in a week, what is her profit? Is she making money or losing money if she sells 20 teddy bears in a week? Explain. [4 marks] b) How many bears did April sell in a week if she made a profit of $560? [5 marks] 8. One leg(side) of a right triangle is 1 cm longer than the other leg(side). The hypotenuse is 9 cm greater than that of the shortest leg. Find the lengths of the three sides. Hint: Draw a Diagram, use the Pythagorean Theorem and the Quadratic formula. Remember to declare the variable and include a conclusion. [8 marks]