Answer the following questions using what you've learned from this unit. Write your responses in the space provided. For questions 1 and 2, you will convert a quadratic function from one form to another. 1. Convert the following function into standard form, y = ax + bx + c. (4 points) y = 2(x -5) (x + 2) Part I: What will be your first step in this process? (2 points) Part II: Carry out your first step and show the resulting function below. (2 points) Part III: Now carry out the final step and write the function in standard form below. (2 points)2. Convert the following function into standard form, y = ax + bx + c. (8 points) y - 3 = -2(x + 1) 3. Solve by factoring: x - 5x - 36 = 0 . Part I: By looking at the equation, which of the following factor combinations will be the correct one for this problem? Explain your choice. (2 points) A. ( x + _)(x + _ ) B. (x - _)(x - _) C. (x + _)(x - _) Part II: Factor the equation. (4 points) Part III: Solve the equation you just factored. (2 points)4. Solve using the quadratic formula: x2 - 4x + 1 = 0. Part I: Write out the quadratic formula using the correct values from the equation. (2 points) Part II: Simplify the quadratic formula to solve this equation. Do not write your answer as a decimal. Instead, leave radicals in your answer. (4 points) 5. Use the quadratic formula to solve: 3x2 + 4x + 2 = 0. Part I: What is the value of the discriminant? What does this tell you about the solutions to the equation? (4 points) Part II: Solve the equation using any method. (4 points)6. On the graph below, plot the following critical points of the function y - 3 = 2(x - 1) i. The vertex (4 points) ii. The y-intercept (4 points) 10- - 10 10 -10- Part II: Does the graph of this function have any x-intercepts? If so, find them. If not, explain how you know. (4 points) Part Ill: Complete the sketch of this graph from the points you've already plotted. (4 points)7. A box is to be formed by cutting square pieces out of the corner of a rectangular piece of a 4" by 6" note card as shown below. The sides will then be folded up to make the box. Part I: (4 points) A. Express the new length of the long side of the note card. once the two corners are removed. B. Express the new width of the short side of the note card, once the two corners are removed. Part II: Write a function AU) that denes the area of the bottom of the box. once the corners are removed and the sides are folded up. [4 pohts) Part III: (3 points} A. Suppose you want the bottom of your box to cover a total area of 'l 6 in2. Set up an equation in standard form that will help you nd the size ()6) of the corner you need to cut in order for your box to have this area. (B POMS} B. Solve this equation and take note of any extraneous solutions. Explain why the answer is extraneous, and clearly state the correct answer. (3 POMS} 3. Use the function y = x2 5x 1:1 to answer the following questions. Part I: What is the yintercept of this function? Express your answer in the form (Ky) . (4 points) Part II: Find the coordinates of the vertex. Express your answer in the form (w). (4 points) Part III: Factor the function to nd the coordinates of the xintercepts of the function's graph. Express your answer in the form (mi) .(4 points) 9. Use the function y = 2x2 + 3x 7' to answer the following questions. Part I: What is the yintercept of this function? Express your answer in the form (Mil . (4 points) Part II: What are the coordinates of the vertex? Express your answer in the form (my) . (4 points) Part III: Use the quadratic formula to find the coordinates of the x-intercepts of the function's graph. Round your answers to the nearest hundredth. Express your answer in the form (x,/) (4 points)