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What are some “real world” applications of the quadratic equation?

What are some “real world” applications of the quadratic equation?. Do Now: What is the equation for the x-value of the vertex of a quadratic equation?. How do we use quadratics with geometric applications?.

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What are some “real world” applications of the quadratic equation?

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  1. What are some “real world” applications of the quadratic equation? Do Now: What is the equation for the x-value of the vertex of a quadratic equation?

  2. How do we use quadratics with geometric applications? • You will often have to use quadratics to solve problems with right triangles (Pythagorean Theorem) or with areas • Things to remember! • Draw a picture if you don’t have one • Write an equation • Solve • Check your answers! Negative values don’t make sense for distance or time!

  3. Examples • In right triangle CTH, hypotenuse CT=6, TH=x, CH=8-x. Write an equation in terms of x that can be used to find TH, solve for x. • A square and a rectangle have the same area. The length of the rectangle is 5 inches more than twice the length of a side of the square. The width of the rectangle is 6 inches less than the length of a side of the square. Find the length of a side of the square.

  4. How do we use quadratics to solve “real world” problems? • You will have to use quadratics to solve problems involving falling objects and constructed stories. • Normally, you will be asked to find: • Maximum height (y-value of vertex) • Time at maximum height (x-value of vertex) • Time to hit the ground (roots) • These problems provide you a function with which to work

  5. Example • Abigail, who has a bionic arm, is crossing a bridge over a small gorge and decides to toss a coin into the stream below for luck. The distance of the coin above the water can be modeled by the function y= -16x2+96x+112, where x measures time in seconds and y measures the height, in feet, above the water. • Find the greatest height the coin reaches before it drops into the water • Find the time at which the coin hits the water.

  6. Summary/HW • What are common types of geometry questions involving quadratics? What are the usual parts of a “real world” question? • HW: pg 98, 1-10 (We will work on some of these in class)

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