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What is the vertex of the quadratic function f(x) = (x - 6) (2x + 2)?

User Koolmees
by
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1 Answer

4 votes

Answer:

the coordinates of the vertex are: (2.5, -24.5)

Explanation:

Recall that when we have a quadratic in its standard form:


f(x)=ax^2+bx+c

the position of the x-coordinate for the vertex can be obtained via:


x_(vertex)=(-b)/(2a)

Then in order to find the vertex, first we write the expression in standard form:


f(x)=(x-6)(2x+2)\\f(x)=2x^2+2x-12x-12\\f(x)=2x^2-10x-12

Now that we have the values for the parameters "
a" and "b" we find the x of the vertex:


x_(vertex)=(-b)/(2a)=(10)/(2*2)=(5)/(2)

Now we use this x-value in the function to find the correspondent y-value of the vertex:


f(x)=2x^2-10x-12\\f((5)/(2) )=2\,((5)/(2) )^2-10((5)/(2) )-12\\f((5)/(2) )=-24.5

Then, the coordinates of the vertex are: (2.5, -24.5)

User SGodoy
by
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