what is the axis of syymetry of the graph f(x)=(x+1)(x+5)

Question

A. x=2

B. x=-1

C. x=-3

D. x=5

Answer 1

(x+1)(x+5) = x^2 +6x +5

take the derivative

f' = 2x +6 = 0

x=-6/2

x=-3 is the axis of symmetry

= -b/2a with a^2+bx+c and a=1,b=7,c=6

or just take the 2 x intercepts, -1 and -5

and average them (-1-5)/2=-3

Answer 2

The axis of symmetry is the vertical line that passes through the vertex so that the right side and left side are mirror images. This line will fall exactly half way between the two points of intersection with the x axis.

These points are found by setting each of the factors equal to 0.

x + 1 = 0. and x + 5 = 0

So x = -1 and x = -5

What number is exactly half way between -5 and -1. The answer is -3. So the axis of symmetry is x = -3

If your problem had not come to you in factored form, you can use the following technique.

If f(x) = x²+ 6 x + 5 the vertex is at x = -b/2a. So the value is -6/(2X1) = -3