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

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> 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      Log On


   

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;
f%28x%29=+x%5E2-2x-4

could someone please help me with this problem.
thank you


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


Simply plug in f%28x%29=0 to get 0=x%5E2-2x-4. The goal now is to solve for 'x'.


Notice that the quadratic x%5E2-2x-4 is in the form of Ax%5E2%2BBx%2BC where A=1, B=-2, and C=-4


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


x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


x+=+%28-%28-2%29+%2B-+sqrt%28+%28-2%29%5E2-4%281%29%28-4%29+%29%29%2F%282%281%29%29 Plug in A=1, B=-2, and C=-4


x+=+%282+%2B-+sqrt%28+%28-2%29%5E2-4%281%29%28-4%29+%29%29%2F%282%281%29%29 Negate -2 to get 2.


x+=+%282+%2B-+sqrt%28+4-4%281%29%28-4%29+%29%29%2F%282%281%29%29 Square -2 to get 4.


x+=+%282+%2B-+sqrt%28+4--16+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-4%29 to get -16


x+=+%282+%2B-+sqrt%28+4%2B16+%29%29%2F%282%281%29%29 Rewrite sqrt%284--16%29 as sqrt%284%2B16%29


x+=+%282+%2B-+sqrt%28+20+%29%29%2F%282%281%29%29 Add 4 to 16 to get 20


x+=+%282+%2B-+sqrt%28+20+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%282+%2B-+2%2Asqrt%285%29%29%2F%282%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%282%29%2F%282%29+%2B-+%282%2Asqrt%285%29%29%2F%282%29 Break up the fraction.


x+=+1+%2B-+1%2Asqrt%285%29 Reduce.


x+=+1%2B1%2Asqrt%285%29 or x+=+1-1%2Asqrt%285%29 Break up the expression.


So the solutions are x+=+1%2B1%2Asqrt%285%29 or x+=+1-1%2Asqrt%285%29


which approximate to x=3.236 or x=-1.236


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


In order to graph y=x%5E2-2x-4, we need to plot some points.


Let's find y when x=-2
(Note: you can start with any x-value):


y=x%5E2-2x-4 Start with the given equation.


y=%28-2%29%5E2-2%28-2%29-4 Plug in x=-2.


y=4-2%28-2%29-4 Square -2 to get 4.


y=4%2B4-4 Multiply -2 and -2 to get 4.


y=4 Combine like terms.


So when x=-2, then y=4.


So we have the point .


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


Let's find y when x=-1:


y=x%5E2-2x-4 Start with the given equation.


y=%28-1%29%5E2-2%28-1%29-4 Plug in x=-1.


y=1-2%28-1%29-4 Square -1 to get 1.


y=1%2B2-4 Multiply -2 and -1 to get 2.


y=-1 Combine like terms.


So when x=-1, then y=-1.


So we have the point .


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


Let's find y when x=0:


y=x%5E2-2x-4 Start with the given equation.


y=%280%29%5E2-2%280%29-4 Plug in x=0.


y=0-2%280%29-4 Square 0 to get 0.


y=0%2B0-4 Multiply -2 and 0 to get 0.


y=-4 Combine like terms.


So when x=0, then y=-4.


So we have the point .


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


Let's find y when x=1:


y=x%5E2-2x-4 Start with the given equation.


y=%281%29%5E2-2%281%29-4 Plug in x=1.


y=1-2%281%29-4 Square 1 to get 1.


y=1-2-4 Multiply -2 and 1 to get -2.


y=-5 Combine like terms.


So when x=1, then y=-5.


So we have the point .


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


Let's find y when x=2:


y=x%5E2-2x-4 Start with the given equation.


y=%282%29%5E2-2%282%29-4 Plug in x=2.


y=4-2%282%29-4 Square 2 to get 4.


y=4-4-4 Multiply -2 and 2 to get -4.


y=-4 Combine like terms.


So when x=2, then y=-4.


So we have the point .


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


Let's find y when x=3:


y=x%5E2-2x-4 Start with the given equation.


y=%283%29%5E2-2%283%29-4 Plug in x=3.


y=9-2%283%29-4 Square 3 to get 9.


y=9-6-4 Multiply -2 and 3 to get -6.


y=-1 Combine like terms.


So when x=3, then y=-1.


So we have the point .


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


Let's find y when x=4:


y=x%5E2-2x-4 Start with the given equation.


y=%284%29%5E2-2%284%29-4 Plug in x=4.


y=16-2%284%29-4 Square 4 to get 16.


y=16-8-4 Multiply -2 and 4 to get -8.


y=4 Combine like terms.


So when x=4, then y=4.


So we have the point .


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

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


Table of Values:





xy
-24


-1-1


0-4


1-5


2-4


3-1


44

Now let's plot the points:




Graph:


Now draw a curve through all of the points to graph y=x%5E2-2x-4:


Graph of y=x%5E2-2x-4


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

Also, feel free to check out my website.

Jim