APPLICATIONS OF Quadratic Equations STEPS: 1) Underline the key information. 2) Draw a diagram if necessary. 3) Assign the value of the unknown quantity to “x”(or appropriate variable ex. t for time) 4) Create a function “y”(or appropriate variable) in terms of “x”. 5) Create a quadratic equation in terms of “x” in standard form. 6) Solve the quadratic equation by factoring or using the quadratic formula. 7) If a maximum or minimum value is required, solve using vertex form, not using a quadratic equation. EXAMPLES OF EACH TYPE OF APPLICATION: Ex. 1: Integer Question The sum of the squares of two consecutive even integers is 6052. Determine the integers. SOLUTION: ...Example CONTINUED Ex.2) Height with respect to time A football is thrown upward at an initial velocity of 12m/s from a height of 1.5m above the ground. a) Determine the equation of the height of the ball. b) What is the height of the ball after 1s? ...Example CONTINUED c) After how many seconds does the ball land? ...Example CONTINUED d) What is the maximum height of the ball and when does this occur? ...Example CONTINUED e) When is the ball at a height of 1m? ...Example CONTINUED f) If the football was thrown on the moon[g = 1.62 m / s],2 when would it hit the ground? Example 3: Area Problem 3A: A rectangluar swimming area at a beach is enclosed by a 240m safety line on three sides. If the area of m2 the swimming area is 6912 determine the length and the width of it. ...Example CONTINUED Area Problem 3B: A picture frame measures 40cm by 75cm. A new frame is made by increasing each side the same amount such that the area of this new frame is 1.7 times the old one. Determine the dimensions of the new frame to the nearest tenth. ...Example CONTINUED Example 4: Volume An open topped box is to be constructed from a square piece of cardboard by removing a square with side length 8cm from each corner and folding up the edges. The resulting box its to have a volume of 512 3 cm dimensions . Find the of the original piece of cardboard. ...Example CONTINUED Example 5: Revenue A ferry operator takes tourists to an island. The operator carries an average of 500 people per day for a round-trip fare of $20. The operator estimates that for each $1 increase in fare, 20 fewer people will take the trip. a) What fare will maximize the number of people taking the ferry? ...Example CONTINUED b) What price will provide a revenue of $9520 per day?

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# 6.5 APPLICATIONS OF Quadratic Equations