SOLUTION: use the quadratic formula to determine the x-intercepts (if any) of the following function. Then evaluate the function for several values of x, and use the resulting points to gra

Question 335943: use the quadratic formula to determine the x-intercepts (if any) of the following function. Then evaluate the function for several values of x, and use the resulting points to graph the function. Show your work;

could someone please help me with this problem.
thank you

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Finding the x-intercepts:

Simply plug in to get . The goal now is to solve for 'x'.

Notice that the quadratic is in the form of where , , and

Let's use the quadratic formula to solve for "x":

Start with the quadratic formula

Plug in , , and

Negate to get .

Square to get .

Multiply to get

Rewrite as

Add to to get

Multiply and to get .

Simplify the square root (note: If you need help with simplifying square roots, check out this solver)

Break up the fraction.

Reduce.

or Break up the expression.

So the solutions are or

which approximate to or

So the x-intercepts are roughly (3.236, 0) and (-1.236, 0)

In order to graph , we need to plot some points.

Let's find y when
(Note: you can start with any x-value):

Start with the given equation.

Plug in .

Square to get .

Multiply and to get .

Combine like terms.

So when , then .

So we have the point

.

----------------------------------------------------

Let's find y when :

Start with the given equation.

Plug in .

Square to get .

Multiply and to get .

Combine like terms.

So when , then .

So we have the point

.

----------------------------------------------------

Now let's make a table of the values we just found.

Table of Values:



x y
-2 4
-1 -1
0 -4
1 -5
2 -4
3 -1
4 4

Now let's plot the points:

Graph:

Now draw a curve through all of the points to graph :

Graph of

If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my website.

Jim
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