For the equation y = x² + 2x - 15 the variables are a=1, b=2, c=-15

y-intercept (where x = 0):
    y = 1(0)² + 2(0) - 15 = -15

vertex format (completing the square):
    y = x² + 2x + 1 - 15 - 1 => y = (x + 1)² - 16 (vertex is (-1, -16))

x-intercept format ("factored"):

Find factors of -15 (c) whose sum is 2 (b)

Pairwise factors of -15

Candidate	Factor 1	Factor 2	Sum
1	-1	15	14
2	1	-15	-14
3	-3	5	2
4	3	-5	-2

The candidate highlighted above gives us the factors.
    y = (x - 3)(x + 5) (using zero product property, the x-intercepts are 3 and -5)

Graph the three versions of the highlighted equations (using Desmos.com here) and confirm they are equivalent. ALSO, confirm that the y- and x-intercepts are correct, as well as the vertex: