Explanation:
I am not sure, what is the level of math for you currently.
do you do differentiation and derivatives already ?
because that is how I find "extreme points" and "turning points" of a function right away.
the vertex is the turning point for a quadratic parabola.
that means the point where the slope (= the first derivative) of the function is 0.
and that is also where the axis of symmetry is.
8x - 8 = 0
8x = 8
x = 1 (axis of symmetry).
y = 4×1² - 8×1 = 4 - 8 = -4
so, the vertex is (1, -4)
in case you don't understand derivatives yet, there is a shortcut for this for quadratic equations (fyi - in fact, the generic result of the first derivative) :
y = ax² + bx + c
the x value for the axis is then
x = -b/(2a)
in our case
a = 4
b = -8
x = - -8/8 = 8/8 = 1
and then y is calculated as above.