Verified Answer :

carlosego

For this case we have the following function:
 \(f(x) = -5x^2 - 20x - 10\)
 To find the axis of symmetry, the first thing to do is to derive the function.
 We have then:

 \(f '(x) = -10x - 20\)
 Equaling zero we have:

 \(-10x - 20 = 0\)
 We clear the value of x.

 We have then:

 \(-10x = 20 x = -20/10 x = -2\)
 Answer:

 The axis of symmetry is given by:

 x = -2

Answer:

x=  -2 is the axis of symmetry for \(f(x) = -5x^2-20x-10\)

Step-by-step explanation:

A quadratic equation is in the form of \(y =ax^2+bx+c\) .......[1],

then the axis of symmetry is given by:-

\(x = -\frac{b}{2a}\)                   ....[2]

As per the statement:

\(f(x) = -5x^2-20x-10\)

On comparing with equation [1] we have;

a = -5, b = -20 and c = -10

Substitute these values in [2] we have;

\(x = -\frac{-20}{2 \cdot (-5)}\)

⇒\(x = -\frac{-20}{-10}\)

Simplify:

x =  -2

Therefore, the axis of symmetry for the given function is, x= -2.

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