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

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) (Show Source): You can put this solution on YOUR website!
To find the roots of , set the entire function equal to zero

Set the function equal to zero

Factor the left side (note: if you need help with factoring, check out this solver)

Now set each factor equal to zero:
or

or Now solve for x in each case

So the roots are:
or

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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

Looking at , we can see that and .

Plug and into the formula.

Multiply

Negate -4 to get 4

Reduce

So the x-coordinate of the vertex is

To find the y coordinate, simply plug in into to evaluate

Let's evaluate

Start with the given function.

Plug in . In other words, replace each x with 2.

Evaluate to get 4.

Multiply -4 and 2 to get -8

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)

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