Concept Math Map #3

Concept Math Map #3

1. C.2 Solving Quadratic Functions

   • Steps to Solving Polynomial Equations by Factoring
     • 1. Set the polynomial equal to zero. 2. Factor the polynomial completely. 3.Set each of the factors equal to zero and solve. 4.Check your answers in the original equation.
   • Steps to Solving Quadratic Equations Using the Square Root Property
     • 1.Isolate the squared variable expression 2.Use the square root property to undo the square. Use on the side away from the variable 3.Rewrite as two equations and solve 4.Check answer(s) in the original equation. Be sure that answers are within the domain of the model and that they make sense in the context of the problem.
   • Solving Quadratic Equations by Completing the Square
     • 1.Isolate the variable terms on one side of the equation. 2.If the coefficient of x^2 is not 1, divide both sides of the equation by the coefficient of x^2. 3.Take half of the coefficient of x, then square it. Add this number to both sides of the equation.4.Factor the quadratic into the square of a binomial.5. Solve using the square root property.6. Check your answers in the original equation
   • Steps to Solving Equations Using the Quadratic Formula
     • 1.Set the quadratic equal to zero. 2.Put the quadratic into standard form.3.Substitute the values of a, b, and c into the quadratic formula.4. Simplify the quadratic formula.5. Check answers in the original equation

2. 5.2 Quadratic Functions & Their Graphs

   • Vertex Form of a Parabola
     • y=a(x-h)^2+k skinner if... a>1 Wider if... 0 Vertex (h,k)

3. 5.3 Maxima and Minima of Quadratics

   • General Form:f(x)=ax^2+bx+c
   • Standard Form: f(x)= a(x-h)^2+k
   • Max is Faced Down (Parabola)
   • Min is Faced Up (Parabola)

4. 5.4 Quadratic Equations

   • X- Intercepts
     • ax^2+bx+c
   • Y- Intercept
     • Set x=0

5. Inverse Variation

   • Y=kx
     • Inverse Variation: Examples: Instead of charging an $8 entrance fee, the students decide that each student attending the party will pay an equal share of the rental cost of the hall ($800 for the evening for the hall). The maximum capacity of the hall is 325 people. (a) How much would it cost per student if 40 students attend? If 125 students attend? 800/40=20 It would cost $20 per student if 40 students attend the party. 800/125=6.4It would cost $6.40 per student if 125 students attend the party.(b)Find a model that gives the cost per student attending the party.C(n)=800/n Where C is the cost per student, and n is the number of students attending this event.  (c) What is a reasonable domain and range for the model?  -Domain; there has to be at least on person and at most 325 people {1,325} -Range {2.47,800}

6. Simplifying Rational Functions

   • AC/BC=A/B

7. Multiplying & Dividing Rational Expressions

   • Multiplying
     • 1. Factor the numerators and denominators completely. 2. Simplify by dividing out common factors in the numerator and the denominator. 3. Multiply the remaining factors of the numerators together and multiply the remaining factors of the denominator together.
   • Divide
     • Invert and multiply

8. Adding & Subtracting Rational Expressions

   • Adding
     • 1.Factor the denominators and find the LCD (if necessary). 2.Rewrite each rational expression with the common denominator.3.Add or subtract, and then simplify
   • Subtracting
     • 1.Factor the denominators and find the LCD (if necessary). 2.Rewrite each rational expression with the common denominator. 3.Add or subtract, and then simplify