Answer :

carlosego
For this case we have the following function:
 [tex]f(x) = -5x^2 - 20x - 10 [/tex]
 To find the axis of symmetry, the first thing to do is to derive the function.
 We have then:
 [tex]f '(x) = -10x - 20 [/tex]
 Equaling zero we have:
 [tex]-10x - 20 = 0 [/tex]
 We clear the value of x.
 We have then:
 [tex]-10x = 20 x = -20/10 x = -2 [/tex]
 Answer:
 The axis of symmetry is given by:
 x = -2

Answer:

x=  -2 is the axis of symmetry for [tex]f(x) = -5x^2-20x-10[/tex]

Step-by-step explanation:

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

then the axis of symmetry is given by:-

[tex]x = -\frac{b}{2a}[/tex]                   ....[2]

As per the statement:

[tex]f(x) = -5x^2-20x-10[/tex]

On comparing with equation [1] we have;

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

Substitute these values in [2] we have;

[tex]x = -\frac{-20}{2 \cdot (-5)}[/tex]

⇒[tex]x = -\frac{-20}{-10}[/tex]

Simplify:

x =  -2

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