Quad.applications
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
» We can construct quadratic equations in geometrical problems as well, primarily those involving area or similar triangles
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!!!
» 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)
» 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.
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?
“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.
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
» -16x 2 +96x+112=0 next: Divide by -16
» x 2 -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
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
