i find the equation of the above parabola ii find the equati

(i) find the equation of the above parabola?

(ii) find the equation of the axis of symmetry.

(iii) find the co-ordinates of the vertex.

please give explanations thanks so much

cheers

(i) Since the parabola cuts the x-axis at -2 and 2, x-(-2) and x-2 are the factors of the equation of the parabola.

Then the equation of parabola is,
y = a(x+2)(x-2) ... (1)

Now the given parabola passes through (3,10) =(x,y)

10 = a ( 3+2) (3-2)

10 = a(5)(1)

a = 10/5 = 2

Substituting this in (1), we get

y = 2(x+2)(x-2) = 2(x² - 4) = 2x²- 8

(ii) The abobe equation can be written as,

y = 2 (x- 0)²-8

Comparing this with

y = a (x-h)²+k, we get

h = 0 and y =-8

So the axis of symmetry is,

x=h (formula)

So, x=0

(iii) From part (ii),

vertex = (h,k) = (0,-8)