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Find the equation of the axis of symmetry for this function.
f(x) = - 4 {x}^(2) + 16x + 47

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You have the followin function:

f(x) = -4x² + 16x + 47

take into account that the axis of symmetry of the previous function is given by the value of the x-coordinate of the vertex of the function.

Such vertex is given by teh following expression:

x = -b/2a

where a and b are the coefficients of the genereal form of a quadratic function, given by:

f(x) = ax² + bx + c

by comparin the previous expression witht he given f(x) you have that:

a = -4

b = 16

replace the previous values into the expression for x:

x = -16/(2(-4))

x = -16/(-8)

x = 2

for x = 2, there is the vertex of the function. A vertical line that crosses the x axis at x= 2 is the axis of symmetry of the given function.

The axis of symmetry is then:

x = 2

User Samuel Seda
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