Answer:
g(x) = x² + 4x + 1
Explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Here (h, k) = (- 2, - 3), thus
y = a(x + 2)² - 3
To find a substitute (2, 13) into the equation
13 = a(2 + 2)² - 3
13 = 16a - 3 ( add 3 to both sides )
16 = 16a ( divide both sides by 16 )
a = 1, hence
g(x) = (x + 2)² - 3 ← expand factor and simplify
= x² + 4x + 4 - 3
g(x) = x² + 4x + 1