Question

What is the axis of symmetry for f(x) = −5x2 − 20x − 10

Answer 1

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

Explanation:

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

then the axis of symmetry is given by:-

`x = -(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 = -(-20)/(2 \cdot (-5))`

⇒
`x = -(-20)/(-10)`

Simplify:

x = -2

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

Answer 2

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