N7.+Given+a+verbal,+algebraic,+graphical,+or+tabular+description+of+a+quadratic+function,+provide+any+of+the+other+three+ways+of+describing+it.


 * N7. Given a verbal, algebraic, graphical, or tabular description of a quadratic function, provide any of the other three ways of describing it. **

=**1. What you need to understand.**=

This means that in the equation, the ax 2 +bx+c=0, the ax must be to the power of 2, nothing more or less.
 * A quadratic function is an equation in which the highest power of a number is a square. **


 * Quadratic functions can be shown in many different ways. It may be a table, graph, equation, or verbal. **

// Table ://



//Graph://



//Equation:// (x+2)(x+3)=0 or x 2 +5x+6=0

//Verbal:// a=1 b=5 c=6, a paragraph explaining a situation how the equation is used.


 * Quadratic equations can be shown in different ways. Factored form, or standard form. These all equal 0. **

Factored: (x+2)(x+3)=0

Standard: x 2 +5x+6=0

=**2**.**Example Problems**=


 * //Given Equation:// x 2 +5x+6=0 **

__ How to get graph: __ Simply use your graphing calculator. Go to the graphing feature and put in the equation. The calculator will create the graph for you.

__ How to get table: __ First, you must put the equation into your graphing calculator. Your calculator will automatically make a table with x and y coordinates.

__ How to get verbal: __ The standard form of quadratic equations is a x 2 +bx+c=0. Using this equation, your a is 1, your b is 5, and your c is 6. All you must do is refer to the equation to see which coefficients are which.


 * // Given Gra //// ph: //**

__ How to get equation: __ See what your x- intercepts are. (When y=0) These are your solutions. By using the solutions, you can put this into a factored equation. For this graph, the x intercepts are (0, -3) and (0,-2) So, you take the y coordinate, switch the sign, and put it in the form (x+2)(x+3)=0. From there, to put it in standard form, all you must do is expand it. The easiest method of expansion is the FOIL method (Front, outside, inside, last) After doing that, you find your equation in standard form, ax 2 +bx+c=0.



__ How to get table: __ If you are given a picture of a graph, you must first follow the steps to find the equation. Then, you put the equation into your calculator to make the table for you. __ How to get verbal: __ Again, you must follow the steps to find the equation before you can find out what a, b, and c are. Depending on the type of quadratic equation it is, it may be the path of a bouncing ball. shape of a bride, etc.

Given Table: How to get equation

To get the equation, you need to know a few things.

-When y=0 -When x=0 and what x's are when y=0

The table above shows all three.

When y is 0, the x's that are shown are -2 and -3. When x is 0, the y shown is 6.

Going by the ax 2 +bx+c, you also need to know basic factoring.

Since both x numbers are negative to begin with, both numbers will be switched to positive in the factored form.

(x+2)(x+3)

x*x=x 2

x*2=2x x*3=3x 2*3=6

Putting them all together, you would get x 2 +5x+6

__ How to get graph __ To get the graph, simply put the equation found beforehand into your graphing calculator and use the graphing function.

__ How to get verbal __

The equation needs to be found before you can find the verbal. x 2 +5x+6

a=1 b=5 c=6

Since x 2 is at a unit of 1, the a is 1. Since 5x is at a unit of 5, the b is 5. And since 6 is at a unit of... well.... 6, the c is 6

Given Verbal: a=1 b=5 c=6

How to get graph

The a is what depends if it faces upwards or down. Since it is positive, then the graph will point upwards. The b is what moves the graph left or right. The c is the y intercept, where the graph crosses the y axis. In this case, it would be at 6

How to get table In order to get a table, you need to substitute values for the x variable in the equation.

Substituting 0 for the x value would cause the equation to be y=0 2 +5(0)+6. Simplified it would just be y=6

This means that when x is 0 y is 6. Thus giving you one value for the table.

How to get equation Following the base function of ax 2 +bx+c, all you need to do is plug in the numbers that are given to you in their respective places. x 2 +5x+6

=**3. Common mistakes or misunderstandings:**= -Algebraic errors ( Confusing x with x 2 ) -Arithmetic errors ( Adding where multiplication is supposed to be used, vice versa) -Not realizing that not all graphs will cross not x axis, and not all have solutions so methods can be flawed

=**4. For more information:**= >
 * CPMP Tools
 * http://www.mathsisfun.com/quadratic-equation-solver.html
 * http://www.studystack.com/matching-4767