Completing the Square Quadratic Formula Sec. 1.4 cont. Completing the Square Quadratic Formula

Completing the Square The purpose of completing the square is to develop a perfect square trinomial so you can factor it down to a binomial squared

Steps in completing the square Get the constant on one side by itself and the x2 + bx part on the other. Add to both sides Factor the new trinomial Extract the roots

Ex. 3

Important The leading coefficient must be 1 or you have to divide both sides of the equation by the lead coefficient to make it 1 before completing the square.

Ex. 3x2 – 4x – 5 = 0

Quadratic Formula For ax2 + bx + c = 0

Located under the radical Discriminant b2 – 4ac Located under the radical

The discriminant lets us tell the number of solutions Positive Zero Negative 2 distinct real solutions 1 repeated solution No real solutions

Ex. 4 x2 + 3x = 9

Ex. 5 A bedroom is 3 ft. longer than it is wide. The area is 154 sq. ft. Find the dimensions

Position Equation Gives the height of something falling or thrown into the air.

s = -16t2 + v0t + s0 s is the height in feet of the object at a given time. v0 is the initial (original) velocity ft/s s0 is the original height of the object in ft. t is the time The -16 is acceleration due to gravity in ft/s2

Ex. 6 A construction worker on the 24th floor drops a wrench and yells. Could a person below hear in time to get out of the way?