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Please help:Let f (x) = x^2 + 14x + 36 .What is the vertex form of f (x)?What is the minimum value of f (x)?Enter your answers in the boxes.Vertex form: f (x )= __Minimum value of f (x): __

Please help:Let f (x) = x^2 + 14x + 36 .What is the vertex form of f (x)?What is the-example-1
User Vithani Ravi
by
3.7k points

1 Answer

12 votes
12 votes

Okay, here we have this:

Considering the provided function, we are going to convert it to vertex form and to find the minimum value of f(x), so we obtain the following:

Vertex form:

​f (x) = x^2 + 14x + 36​

y - 36 = x^2 + 14x

y - 36 + (14/2)^2 = x^2 + 14x + (14/2)^2

y - 36 + 49 = x^2 + 14x + 49

y +13 = (x+7)^2

f(x)= (x+7)^2 - 13, This is the function in vertex form.

Minimum value of f (x):

To calculate the minimum then we will find the vertex:

To calculate the minimum then we will find the vertex: x=-b/(2a)

x=-b/(2a)

x=-14/(2*1)

x=-14/2

x=-7

And the y-coordinate will be:

f(-7)=(-7+7)^2 - 13

f(-7)=(0)^2 - 13

f(-7)=- 13

Finally we obtain that the minimum value of f(x) is -13.

Considering the provided function, we are going to convert it to vertex form and to find the

User Simplelenz
by
3.1k points
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