Question

What is the axis of symmetry for f(x)=5(x+7)(x-5)

Answer 1

What is the axis of symmetry for f(x)=5(x+7)(x-5)?  Multiply out this polynomial to obtain the equation of a parabola in the form y = ax^2 + bx + c.

f(x) = 5(x^2 - 5x + 7x -35)

Holding the coefficient 5, we have 1x^2 - 2x - 35.  Here a = 1 and b = -2, and
thus x = -b / (2a) provides the x-coord. of the axis of symm.  It is:

x = -(-2) / (2*1) = 1.

The axis of symmetry is the vertical line x = 1.