Question

Find the x-intercepts of the parabola with vertex (-4,2) and y-intercept (0,-30). Write your answer in this form: (x1, y1),(x2, y2). If necessary, round to the nearest hundredth.

Answer 1

Vertex form of a parabola 
y = a (x - h)^2 + k 

where (h, k) is the vertex 
Substituting the values of h and k.
we get, 

y = a(x + 4)^2 + 2 

substituting in the point (0, -30) for  x and  y
-30 = a (0 + 4)^2 + 2 

solve for a,

-30 = 16 a + 2 
-32 = 16 a 
-2 = a 

y = -2(x + 4)^2 + 2 

Put y = 0 

-2 x^2 - 16 x - 30 = 0 
-2(x^2 + 8 x + 15) = 0 
x^2 + 8 x + 15 = 0 
(x + 3)(x + 5) = 0 

x = -3
x = -5