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) b) 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 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


» 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