Answer:
g(x) = x² + 4x + 5
Step-by-step 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, 1 ), thus
y = a(x + 2)² + 1
To find a substitute (0, 5) ← y- intercept into the equation
5 = a (0 + 2)² + 1 ( subtract 1 from both sides )
4 = 4a ( divide both sides by 4 )
a = 1
g(x) = (x + 2)² + 1 ← in vertex form
Expand parenthesis and simplify
g(x) = x² + 4x + 4 + 1, then
g(x) = x² + 4x + 5 ← in standard form
