Pre-Calculus 11 Quadratic Functions Worksheet. Pre-Calculus 11 Quadratic Functions Worksheet. 1) Sketch each graph and find the y-intercept algebraically: 2) Write the equation of the parabola shown: 3) Write the equation for a parabola that: a) opens up, has been stretched vertically by a factor of 2 and has been shifted 2 units right and 3 units down. b) opens down, has been compressed vertically by a factor of 1 and has been 3 shifted 5 units left and 2 units up. 4) Write an equation for the parabola with the given information: a) vertex (2, 5), congruent to , opening down y = 5 x 2 b) vertex (–4, 0), and passing through (–2, 12) c) vertex (1, 3) and passing through the point (5, 7) d) vertex (–2, –8) and a y–intercept of 4 e) congruent to y = 5(x + 7)2+1 with an axis of symmetry x = 3 and a max value of 5 5) Without graphing, state: i) the vertex, ii) equation of the axis of symmetry, iii) domain and range, iv) y-intercept v) min / max value and where it occurs 6) Sketch the graph of each parabola and label: i) the coordinates of the vertex ii) the equation of the axis of symmetry, iii) the max / min value and where it occurs 7) A farmer has 300m to enclose his livestock as shown. What will the maximum area be? P = 300 = 3 W + 2 L ; 2 L = 300 – 3 W L = 150 – 1.5 W A = LW = (150 – 1.5 W)W = 150 W– 1.5 W2 = – 1.5 W2 + 150 W Now, we have derived a quadratic equation to maximize the area: Look for the vertex: (p, q) ; p = – 150/2(– 1.5) = 50 q = – 1.5 (50)2 + 150 (50) = 3750 The maximum area is 3750 m2 when the W = 50 m and L = 75 m. 8) A theatre company sells tickets for $120 to 100 people. They estimate that for every $5 decrease in price, 10 more people will purchase tickets. What price will yield the maximum revenue? Let x be the number of times that $ 5 decreases. Revenue = ( 100 + 10x)(120 – 5x) = 12000 + 700x – 50x2 = – 50x2 + 700x + 12000 Again, we have derived a quadratic equation to maximize the revenue: Look for the vertex: (p, q) ; p = – 700/2(– 50) = 7 q = – 50 (7)2 + 700 (7) + 12000 = 14450 It seems that we need to decrease the price of $5 seven times: $120 – $5 (7) = $ 120 – $ 35 = $ 85. The maximum revenue will be $14450 if the new price is dropped to $85.

© Copyright 2020