In this case, we'll have to carry out several steps to find the solution.
Step 01:
Parabola equation
y = x² + 10x + 33
vertex form equation = ?
Step 02:
ax² + bx + c
a = 1
b = 10
c = 33
Vertex Form:
y = a ( x - h )² + k
xv = - b / 2a
xv = -10 / 2 * 1
xv = -5
yv = x² + 10x + 33
= (-5)² + 10(-5) + 33
= 8
( -5 , 8)
y = a ( x - h )² + k
h = horizontal coordinate (vertex)
k = vertical coordinate (vertex)
y = a ( x - h )² + k
y = (x - (-5))² + 8
y = (x + 5)² + 8
graph