Write the equation of the parabola in vertex form. vertex (0,3) point (-4,-45)

Y =  a(x-0)^2 + 3

y = ax^2 + 3

plug in the point (-4,-45):-

-45 = (-4)^2 a + 3

-45 =  16a + 3

a = -48/16 = -3

answer is  -3x^2 + 3

Equation of a parabola:
 (y-k) = a(x-h)², where h & k are the pair of the vertex : vertex(h , k).In the example vertex(0.3), hence
y-3 = a(x-0)² →→ y = ax² + 3. Let's calculate the coefficient "a". To that end replace x & y by the given pair: (-4 , -45):

-45 = a(-4)² +3 → -45 = 16a  +3 & a = -3

Finally the equation is y=-3x³ + 3