+ 6 of 7 0 09 Test Your Knowledge 1) Find the vertex of y = 3x2 - 12x - 1. What is the minimum value of f (x)? 2) Given the function f (x) = x2 - 12x + 32. Express f(x) in standard form. Find the vertex? 3) Let f(x) = -3x2 + 6x -2. (a) Express f in standard/vertex form f (x) = a(x - h)2 + k. (b) Find the vertex of f (x). c) At which x value maximum/minimum occurs? d) Find the maximum or minimum value of f. 4) The following is the graph of the function f (x) = -(x + 2)2 - 1. Determine the Domain and Range of the function, give the coordinates of its vertex and axes intercepts. 5) Find the equation of the quadratic function using the given information: The coordinates of the vertex are (-1, 2.5) and the graph is going through the point (2, 1). 6) Write the equation for the graphed quadratic function. Q Search 99+ EV nyhp WMath 1102 -Section 5.1 7) A ball is thrown vertically upward from the ground with an initial velocity of 122 ft/sec. Use the quadratic function h(t) = -164 + 120t + 60 to find how long it will take for the ball to reach its maximum height, and then find the maximum height. 8) A manufacturer sells 500 units per week at 31 dollars per unit. If the price is reduced by one dollar, 20 more units will be sold. a) Let x be the number of 1 dollar decrease in the price. Express the revenue, R, as a quadratic function of x. b) Determine the price per item that maximize the revenue. c) Determine the maximum the revenue 9) You want to build a rectangle with a 60 cm rope . What should be dimensions of a rectangle to maximize its area? Find the maximum area. (Perimeter of rectangle P = 2(1 + w), area of rectangle A = I - w) 10) Write a quadratic function to represent the product of all pairs of numbers whose difference is 12, and use this function to determine the pair of numbers whose product is the smallest. 11) A manufacturer can produce printer paper at a cost of $2 per ream. The paper has been selling for $5 per ream, and at that price, consumers have been buying 4,000 reams a month. The manufacturer is planning to raise the price of the paper and estimates that for each $1 increase in the price, 400 fewer reams will be sold each month. a) Express the manufacturer's monthly profit as a function of the price at which the reams are sold. b) What price corresponds to maximum profit? What is the maximum profit? 12) Complete the square as necessary and state the coordinates of the centre and the (exact) size of the radius, then sketch its graph. x 2 + y2 + x + 2y =0 13) Complete the square as necessary and state the coordinates of the centre and the (exact) size of the radius, then sketch its graph. x2 + y2 +6x =16 Q Search 199+ W