F(x) = -x^2-3x
find f (10)

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    f*(x)-(-x^2-3*x)=0  

STEP

1

:

STEP

2

:

Pulling out like terms

2.1     Pull out like factors :

  fx + x2 + 3x  =   x • (f + x + 3)  

Equation at the end of step

2

:

 x • (f + x + 3)  = 0  

STEP

3

:

Theory - Roots of a product

3.1    A product of several terms equals zero.  

When a product of two or more terms equals zero, then at least one of the terms must be zero.  

We shall now solve each term = 0 separately  

In other words, we are going to solve as many equations as there are terms in the product  

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation:

3.2      Solve  :    x = 0  

 Solution is  x = 0

Equation of a Straight Line

3.3     Solve   f+x+3  = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line  f+x+3  = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when x = 0 the value of f is -3/1 so this line "cuts" the f axis at f=-3.00000

 f-intercept = -3/1  = -3.00000  

Calculate the X-Intercept :

When f = 0 the value of x is -3/1 Our line therefore "cuts" the x axis at x=-3.00000

 x-intercept = -3/1  = -3.00000  

Calculate the Slope :

Slope is defined as the change in f divided by the change in x. We note that for x=0, the value of f is -3.000 and for x=2.000, the value of f is -5.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of -5.000 - (-3.000) = -2.000 in f. (The change in f is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

   Slope     = -2.000/2.000 = -1.000  

Geometric figure: Straight Line

 Slope = -2.000/2.000 = -1.000

 x-intercept = -3/1 = -3.00000

 f-intercept = -3/1 = -3.00000

x = 0

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