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Chapter 5 Practice Test, Sections 1-4 Name ____________________________ Directions: For each section write the objectives that match the problems in that section Show your work for each problem Check your answers on blackboard! Section 1: Objectives: 1. What is the vertex of y 3x 2 24 x 5 . 1. __________________ 2. Write the quadratic function y 2 x 4 9 in Standard Form. 2 2. __________________ 3. Dalco Manufacturing estimates that its weekly profit, P, in hundreds of dollars, can be approximated by the formula P 3 x 2 6 x 10 , where x is the number of units produced per week, in thousands. Find the maximum weekly profit. How many units were produced to get the maximum profit? a) Sketch a graph of the function (label the x- and y-axes with the correct variables from the equation; estimate the y-intercept, which way will the graph open; label the vertex) b) Find the maximum weekly profit. How many units were produced to get the maximum profit? (Hint: is this a quadratic function? If so, how do we find the maximum of a quadratic function?) 3b. __________________ Section 2: Properties of Parabolas Objectives: 4. What is the axis of symmetry for the quadratic function y 6 x 2 8 x 5 . 4. __________________ 5. A manufacturer determines that the number of drills it can sell is given by the formula D 3 p 2 180 p 285 , where p is the price of the drills in dollars. At what price will the manufacturer sell the maximum number of drills? What is the maximum number of drills sold? (Hint: is this a quadratic function? If so, where do we find the maximum on a quadratic graph?) 5. __________________ 6. Graph y x 2 6 x 5 . State vertex, line of symmetry, y intercept. State domain and range. Section 3: Translating Parabolas Objectives: 7. What is the y-intercept of y 3 x 4 8 ? 2 7. _________________ 8. Write the quadratic function y 3x 2 30 x 10 in Vertex Form. 8. __________________ 9. Write the equation of the parabola in Vertex Form. Given vertex is (3, -7) and a point the parabola passes through is (6, 11). 9. __________________ 10. Graph y 3 x 4 2 . Describe the translation. 2 11. Graph𝑦 = 2(𝑥 − 3)2 − 1. Describe the translation. Section 4: Factoring Objectives: 12. 9 x 2 196 13. 8 x 2 10 x 3 14. 10 x 2 36 x 16 15. −𝑥 2 + 5𝑥 − 4 16. 12 x 2 x 6 17. 36 x 3 12 x 2 15 x 18. Problem solve: Firefighters: A smoke jumper jumps from a plane that is 1700 ft above the ground. The function ℎ = −16𝑡 2 + 1700 gives the jumper’s height h in feet at t seconds. How long is the jumper in free fall if the parachute opens at 800 ft?