# Entrance Slip: Quadratics 1)2) 3)4) 5)6) Complete the Square 7)

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Entrance Slip: Quadratics 1)2) 3)4) 5)6) Complete the Square 7)

Section 1.6 Other Types of Equations

Polynomial Equations

Example Solve by Factoring:

Example Solve by Factoring:

Graphing Equations You can find the solutions on the graphing calculator for the previous problem by moving all terms to one side, and graphing the equation. The zeros of the function are the solutions to the problem. X 4 -13X 2 +36=0

A radical equation is an equation in which the variable occurs in a square root, cube root, or any higher root. We solve the equation by squaring both sides.

This new equation has two solutions, -4 and 4. By contrast, only 4 is a solution of the original equation, x=4. For this reason, when raising both sides of an equation to an even power, check proposed solutions in the original equation. Extra solutions may be introduced when you raise both sides of a radical equation to an even power. Such solutions, which are not solutions of the given equation are called extraneous solutions or extraneous roots.

Press Y= to type in the equation. For the negative use the white key in the bottom right hand side. For the use X use X,T,,,,n Graphing Calculator Move all terms to one side. See the next slide Press 2 nd Window in order to Set up the Table. Press the Graph key. Look for the zero of the function – the x intercept.

The Graphing Calculator’s Table Not a solution Is a solution Press 2 nd Graph in order to get the Table.

Solving an Equation That Has Two Radicals 1.Isolate a radical on one side. 2.Square both sides. 3.Repeat Step 1: Isolate the remaining radical on one side. 4.Repeat Step2: Square both sides. 5.Solve the resulting equation 6.Check the proposed solutions in the original equations.

Example Solve:

Equations with Rational Exponents

Example Solve:

Example Solve:

Absolute Value Graphs The graph may intersect the x axis at one point, no points or two points. Thus the equations could have one, or two solutions or no solutions.