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How can we use quadratic equations in real life?

How can we use quadratic equations in real life?. Do Now: Describe the shape of the path of a basketball to the hoop. Where do we see parabolas?. The most common situation in which we find parabolas are falling bodies. Throwing things in the air Falling into water

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How can we use quadratic equations in real life?

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  1. How can we use quadratic equations in real life? Do Now: Describe the shape of the path of a basketball to the hoop.

  2. Where do we see parabolas? • The most common situation in which we find parabolas are falling bodies. • Throwing things in the air • Falling into water • We can construct quadratic equations in geometrical problems as well, primarily those involving area or similar triangles

  3. How do we solve geometrical problems? • Read the question, underline keywords and circle numbers. • Draw a picture and label everything you can. • Make sure you know what is being asked!!! • How can you solve? • Check!!!

  4. In right triangle CTH, hypotenuse CT=6, TH=x, and CH=8-x. • Write an equation in terms of x that can be used to find TH • Solve the equation for x. (Can be a radical)

  5. 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 the side of the square. Find the length of the side of the square.

  6. What could be asked in falling body problems? • Falling body problems have fairly predictable questions associated with them. • How long will it take to hit the ground? • When is the maximum/minimum attained? • What is the maximum/mimium/vertex?

  7. “Real world” 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 distand of the coin above the water can be modeled by the function y=-16x2+96x+112, where x measure 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 below. • Find the time at which the coin hits the water.

  8. a) Greatest height=vertex • Use -b/2a to find x value • -96/[2*(-16)] = -96/-32 = 3 • Plug into original equation • y=-16(3)2+96(3)+112=-16(9)+288+112 • y=-144+400=256 b) Hits water=solve for x • Set equation equal to zero and solve • -16x2+96x+112=0 next: Divide by -16 • x2-6x-7=0 next: Factor • (x-7)(x+1)=0 next: Solve for x • x=7, -1; however, -1 is before the coin was thrown, so the only valid answer is x=7

  9. Summary/HW • If a question asks for the maximum height, how can you find it? If it asks when an object hits the ground, what are you trying to find? • HW: pg 98, 1-10 odd

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