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For f(x) = x2 – 3x – 15 find f(-2) -5 Determine the vertex, axis of symmetry and graph. 2 y x 3 Vertex: (0, 3) Axis of symmetry: x=0 x y -2 -1 7 4 0 1 2 3 4 7 Find the vertex and axes intercepts. y = -3x2 - 6x Vertex: (-1, 3) y-intercept: (0, 0) x-intercepts: (-2, 0) & (0, 0) Find the coordinates of the points of intersection of the graphs with equations y = x2 – 5x + 10 and y = x + 5 (1, 6) and (5, 10) A skateboard manufacturer finds that the cost $C of making x skateboards per day is given by C(x) = x2 – 24x + 244 a) How many skateboards should be made per day to 12 minimize the cost of production? b) What is the minimum cost? $100 A rectangular has a perimeter of 200cm. Let x be the width of the rectangle. Find the maximum area for the rectangle. P=2L+ 2w 200 = 2L + 2x Area = x(100 – x) Area = 100x – x2 100 – x = L The vertex is: 100 – x (50, 2500) x The maximum area is 2500cm2. Find the minimum of f(x) = 2x2 – 6x + 5 x b 2a 6 2(2) 6 2 3 2 2 1 3 3 3 f 2 6 5 2 2 2 2 3 1 , 2 2 State the vertex, equation for the axis of symmetry, y-intercept. y 2 ( x 1) 3 2 Vertex: (1, -3) Axis of symmetry: x = 1 y-intercept: (0, -1) Determine the axis of symmetry and vertex. y = x2 – 4x + 7 Vertex: (2, 3) Axis of symmetry: x=2 For y = x2 – 2x find the • direction the parabola opens • axes intercepts • equation of the axis of symmetry and graph Opens up y-intercept: (0, 0) x-intercepts: (0, 0) & (2, 0) Vertex: (1, -1) Axis of symmetry: x=1 Name the vertex and axis of symmetry. Graph. y = x2 + 8x + 11 Vertex: (-4, -5) Axis of symmetry: x = -4 x y -6 -5 -1 -4 -4 -3 -2 -5 -4 -1 Name the vertex and axis of symmetry. y = x2 – 7 Vertex: (0, -7) Axis of symmetry: x = 0 A manufacturer of barbeques knows that if x of them are made each week then the total cost will be (60x + 800) dollars and the total receipts per week will be (1000x – 3x2) dollars. How many barbeques should be made per week for maximum profits? 157 The height H meters, of a rocket t seconds after it is fired vertically upwards is given by H(t) = 100t – 5t2, t 0. a) How long does it take for the rocket to reach its maximum height? t = 10 seconds b) What is the maximum height reached by the H(10) = 500 meters rocket? c) How long does it take for the rocket to fall back to earth? 20 seconds A manufacturer finds that the profit $P from assembling x bicycles per day is given by P(x) = -x2 + 50x – 200. a) How many bicycles should be assembled per day to maximize the profit? 25 bicycles b) What is the maximum profit? $425 c) What is the loss made if no bicycles are assembled in a day? $200 Find the coordinates of the points of intersection of the graphs with equations y= x2 – 3x + 7 and y = x + 5 (0.589, 5.59) and (3.41, 8.41)