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 oneWrite an equationSolveCheck 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)