Quad.applications

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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
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