SOLUTION: Does the function have a minimum or maximum value. where does the minimum or maximum value occur what is the functions minimum or maximum value f(x)=-2x^2-16x-35

Question 645273: Does the function have a minimum or maximum value.
where does the minimum or maximum value occur
what is the functions minimum or maximum value

f(x)=-2x^2-16x-35

Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!

1.
since is less than zero, the parabola opens downward and has a global value
2. complete the square

Solved by pluggable solver: Completing the Square to Get a Quadratic into Vertex Form

Start with the given equation

Add to both sides

Factor out the leading coefficient

Take half of the x coefficient to get (ie ).

Now square to get (ie )

Now add and subtract this value inside the parenthesis. Doing both the addition and subtraction of does not change the equation

Now factor to get

Distribute

Multiply

Now add to both sides to isolate y

Combine like terms

Now the quadratic is in vertex form where , , and . Remember (h,k) is the vertex and "a" is the stretch/compression factor.

Check:

Notice if we graph the original equation we get:

Graph of . Notice how the vertex is (,).

Notice if we graph the final equation we get:

Graph of . Notice how the vertex is also (,).

So if these two equations were graphed on the same coordinate plane, one would overlap another perfectly. So this visually verifies our answer.

Notice how the vertex is at(,)-global .
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