This is a sketch of the curve with equation y=f(x) the vertex of the curve is at (2,-3)

The vertex of the given curve is the minimum point on the curve.

The vertex is given as:

(a) The vertex of f(x) + 5

The rule of the given transformation is:

So, we have:

Hence, the vertex of f(x) + 5 is (2,2)

(b) The vertex of -f(x)

The rule of the given transformation is:

So, we have:

Hence, the vertex of -f(x) is (2,3)

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Step-by-step explanation:

(a)

Given f(x) then f(x) + c represents a vertical translation of f(x)

• If c > 0 then a shift up of c units

• If c < 0 then a shift down of c units

f(x) + 5 represents a shift up of 5 units, thus

(2, - 3 ) → (2, - 3 + 5 ) → (2, 2 )

(b)

Given f(x) then - f(x) represents a reflection of f(x) in the x- axis

Under a reflection in the x- axis

a point (x, y ) → (x, - y ), thus

(2, - 3 ) → (2, 3 )

the answer is 4.8 units on e2020.

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step-by-step explanation: