Question

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

Answer 1

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.

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