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), ho

002

2

1htvgt

Equation

• h = • g = force due to gravity• t = time (seconds) • ho = initial height

• V0 = initial velocity

002

2

1htvgt

• 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 aA2 + bA + c = 0.

• Look for the actual variable A first (or, what part that will represent A)

• Ex. Solve the quadratic (x2 + 2x)2 – 7(x2 + 2x) – 8 = 0

• What phrase can represent A?

• Ex. Solve the quadratic like equation (x2 – 6x)2 + 4(x2 – 6x) – 5 = 0

• Assignment• Pg. 94• 46-53, 57-67 odd