Gravity, Technology, Quadratic Like Equations

An object near the surface of earth is under the influence of gravity We can model this by using a quadratic equation

Properties Exclude air resistance and mechanical forces – Simpler version Only applicable for short distances – IE, not launching a rocket into space or satellite in a low orbit h = g = force due to gravity; t = time (seconds), h o

Equation h = g = force due to gravity t = time (seconds) h o = initial height V 0 = initial velocity

Example. You stand at the top tier of seats in a stadium, and decide to throw a ball down to ground level. The ball starts with an upward velocity of 90ft/s, and is 65 feet above ground at the moment you throw the ball. When does the ball hit land?

Using your Calculator For the previous problem, we can use our calculator to help us plot or graph the motion represented by the model Look further into solutions and behavior

Example. Using the previous problems, locate the roots of the quadratic. What is the shape of the quadratic?

Quadratic-Like Equations Some equations can be written in a form similar to quadratics Solve just like we do with quadratics – Factor – Zero Product Property

Quadratic-Like = an equation which can be written as aA 2 + bA + c = 0. Look for the actual variable A first (or, what part that will represent A)

Ex. Solve the quadratic (x 2 + 2x) 2 – 7(x 2 + 2x) – 8 = 0 What phrase can represent A?

Ex. Solve the quadratic like equation (x 2 – 6x) 2 + 4(x 2 – 6x) – 5 = 0

Assignment Pg , odd