Transcript What are some “real world” applications of the quadratic

What are some “real
world” applications of
the quadratic
equation?
Do Now: What is the equation for
the x-value of the vertex of a
quadratic equation?
How do we use quadratics
with geometric
applications?
You will often have to use
quadratics to solve problems with
right triangles (Pythagorean
Theorem) or with areas
Things to remember!
Draw a picture if you don’t have one
Write an equation
Solve
Check your answers! Negative values
don’t make sense for distance or time!
Examples
In right triangle CTH, hypotenuse
CT=6, TH=x, CH=8-x. Write an
equation in terms of x that can be
used to find TH, solve for x.
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 a
side of the square. Find the length
of a side of the square.
How do we use quadratics
to solve “real world”
problems?
You will have to use quadratics to solve
problems involving falling objects and
constructed stories.
Normally, you will be asked to find:
Maximum height (y-value of vertex)
Time at maximum height (x-value of vertex)
Time to hit the ground (roots)
These problems provide you a function
with which to work
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
distance of the coin above the water can be
modeled by the function y= -16x2+96x+112,
where x measures 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
Find the time at which the coin hits the water.
Summary/HW
What are common types of
geometry questions involving
quadratics? What are the
usual parts of a “real world”
question?
HW: pg 98, 1-10 (We will work
on some of these in class)