can you please describe a way to find the exact coordinates of the vertex of a parabola given by...?

Question

f(x)= (x + a)(x - a)

please explain it at algebra/algebra 2 level...

cause i never heard of y = A(x-h)² + k

Answer 1

The vertex form of the equation of a parabola is

y = A(x-h)² + k where (h,k) are the coordinates of the vertex.

Your equation is

f(x) = (x + a)(x - a)

Multiply out the right side:

f(x) = x² - a²

which may be written

f(x) = 1(x-0)² + (-a²)

So the vertex of this parabola is at (0, -a²)

Answer 2

f(x) =y = (x+a)(x-a)

f(x) = x^2 - a^2

The coordinates of vertex of parabola, f(x) = ax^2 + bx + c

are ( -b/2a, f(-b/2a))

here a = 1, b= 0 and c = -a^2

-b/2a = 0

f(0) = -a^2

so vertex coordinates are (0, - a^2)