Identifying Important Parts on Calculator 2nd calc—then select max or min
Completing the Square Used to go from standard form to (h,k) form or to get the equation in the form of a perfect square to solve Steps: 1.Move the constant 2.Factor out the # in front of x 2 3.Take ½ of middle term and square it 4.Write in factored form for the perfect sq. trinomial 5.Add to both sides (multiply by # in front) 6.Move constant back to get in (h,k) form
When solving Graphing—not always best unless you have exact answers Factoring—not every polynomial can be factored Quadratic Formula—always works Square Root method—may have to complete the square first
Solving using Quadratic formula Must be in standard form Identify a, b, and c
Solving Quadratics using the Sq. Rt. method Useful when you have x 2 = constant or a perfect sq. trinomial ex. (x-3) 2 =constant 1.Get the x 2 by itself 2.Take the square rt. of both sides 3.Don’t forget + or – in your answer!!!
Quadratic Inequalities Graphing quadratic inequalities in 2 variables: Steps: Graph the related equation Test a point not on the graph of the parabola Shade region that contains the point if it makes the inequality true or shade the other region if it does not make the inequality true Ex.
Solving Quadratic Inequalities Solving Quadratic Inequalities in one variable: May be solved by graphing or algebraically. To solve by graphing: Steps: Put the inequality in standard form Find the zeros and sketch the graph of the related equation identify the x values for which the graph lies below the x-axis if the inequality sign is < or identify the x values for which the graph lies above the x-axis if the inequality sign is > or
Solve by graphing Solutions:_______________________
To solve algebraically: Steps: Solve the related equation Plot the zeros on a number line—decide whether or not the zeros are actually included in the solution set Test all regions of the number to determine other values to include in the solution set