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

» -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

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