SOLUTION: Sketch the graph, using the function and three points: two roots and the turning point. b. f(x) = x^2 -4x -5

Algebra ->  Graphs -> SOLUTION: Sketch the graph, using the function and three points: two roots and the turning point. b. f(x) = x^2 -4x -5      Log On


   

Question 118378: Sketch the graph, using the function and three points: two roots and the turning point.

b. f(x) = x^2 -4x -5
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
To find the roots of f%28x%29=x%5E2-4x-5, set the entire function equal to zero

x%5E2-4x-5=0 Set the function equal to zero


%28x-5%29%28x%2B1%29=0 Factor the left side (note: if you need help with factoring, check out this solver)



Now set each factor equal to zero:
x-5=0 or x%2B1=0

x=5 or x=-1 Now solve for x in each case


So the roots are:
x=5 or x=-1

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Now let's find the vertex (ie the turning point)

To find the x coordinate of the vertex, simply use this formula x=-b%2F2a

Looking at f%28x%29=x%5E2-4x-5, we can see that a=1 and b=-4.




x=-%28-4%29%2F2%281%29 Plug a=1 and b=6 into the formula.

x=-%28-4%29%2F2 Multiply

x=4%2F2 Negate -4 to get 4

x=2 Reduce


So the x-coordinate of the vertex is x=2


To find the y coordinate, simply plug in x=2 into f%28x%29=x%5E2-4x-5 to evaluate f%282%29



Let's evaluate f%282%29


f%28x%29=x%5E2-4x-5 Start with the given function.


f%282%29=%282%29%5E2-4%282%29-5 Plug in x=2. In other words, replace each x with 2.


f%282%29=%284%29-4%282%29-5 Evaluate %282%29%5E2 to get 4.


f%282%29=%284%29-8-5 Multiply -4 and 2 to get -8


f%282%29=-9 Now combine like terms

So the vertex is (2,-9)



Now let's graph these three points






Now connect the points with a parabola (note: the more points you plot the more accurate the graph is)