SOLUTION: Sketch the graph, using the function and three points: two roots and the turning point. a. f(x) = x^2 + 6x

SOLUTION: Sketch the graph, using the function and three points: two roots and the turning point. a. f(x) = x^2 + 6x - 16

Question 118377: Sketch the graph, using the function and three points: two roots and the turning point.

a. f(x) = x^2 + 6x - 16
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

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

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

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

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 -3.

Evaluate to get 9.

Multiply 6 and -3 to get -18

Now combine like terms

So the vertex is: (-3,-25)

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

Summary:

So our roots are

or

and our vertex is at the point

(-3,-25)

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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