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mash [69]
3 years ago
13

Which function in vertex form is equivalent to f(x) = 4 + x2 – 2x? f(x) = (x – 1)2 + 3 f(x) = (x – 1)2 + 5 f(x) = (x + 1)2 + 3 f

(x) = (x + 1)2 + 5
Mathematics
1 answer:
melamori03 [73]3 years ago
7 0

Answer:  First Option

f (x) = (x-1) ^ 2 + 3

Step-by-step explanation:

Quadratic quadratic functions have the following form:

f (x) = (x-h) ^ 2 + k

Where the point (h, k) is the vertex of the function.

For a quadratic function of the form f (x) = ax ^ 2 + bx + c the vertex of the function is at the point (-\frac{b}{2a}, f(\frac{-b}{2a}))

In this case the function is: f(x) = 4 + x^2 - 2x\\\\f(x)=x^2 -2x +4

Then:

a=1\\b=-2\\c=4

The vertex is:

(-\frac{(-2)}{2(1)}, f(\frac{2}{2(1)}))

(1, f(1))

Note that

f(1) = (1)^2 -2(1) +4\\\\f(1)=1-2+4=3

Therefore the vertex is the point (1, 3)

Finally we have that h=1,\ k=3

The function in vertex form is :

f (x) = (x-1) ^ 2 + 3

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