f(x)=x^2-x-6

Question

I want to graph this equation into a parabola.

Answer 1

The function f is a parabola.    The standard quadratic form is  a x² + b x +c.    So for this case

a =1,  b= -1, c = -6    The x coordinate of the vertex is -b/2a  =   1/2.  The y coordinate of the vertex can be

found by substituting back into  x² -x =6.   It works out to be -25/4

 So the vertex is located at (1/2 , -25/4).   Since a =1, this means that f can be written in vertex form as:

 

  f(x) =  ( x - 1/2)² - 25/4         an upward opening parabola with vertex at (1/2, - 25/4)

 

This should make graphing it easy.

Answer 2

Hi Chinatha,

 

Let's write the coefficients first

a=1, b=-1, c=6

 

a=1 so the graph will open upwards. 

line of symmetry is x=-b/2a 

=-(-1/2*1)

=1/2 this is also the minimum of the function. The y value at this x will be the y-coordinate of the vertex.

plug in 1/2 for x to find that

= (1/2)^2 - 1/2 - 6

= -6.25

So the vertex is at (0.5, -6.25)

Now we need to find the roots of the equation, where f(x) = 0.

x^2 - x - 6 = 0 (the equation can be factored)

(x - 3)(x + 2) = 0

x - 3 = 0

x = 3

x + 2 = 0

x = -2

So, the roots are x={-2, 3}

 

I think you can easily graph it now. Let me know if you have any questions.

Answer 3

There are two methods:

 

1) Plot every single point, which will take forever

2) Find the intercepts and vertex, which are used as guides to drawing the parabola

 

We will use method two.

 

To find the x-intercepts, set f(x)=0 and solve for x.  In some cases, you may need to use the quadratic formula.

 

(x - 3)(x + 2) = 0

 

x = 3       and         x = -2

 

x-intercepts are (-2, 0) and (3, 0).

 

 

To find the y-intercept, evaluate f(0).

 

y-intercept is (0, -6)

 

 

Next, find the vertex.  To find the x-coordinate of the vertex, we use the average of the x-intercepts.

 

(3 + (-2)) / 2 = 1 / 2

 

 

Then to find the y-coordinate of the vertex, evaluate f(1/2).

 

Here are your crucial points:

 

x-intercepts: (-2, 0) and (3, 0)

y-intercept: (0, -6)

vertex: (1/2 , f(1/2))

 

Plot these points on a coordinate grid, and connect them to form a parabola.