f(x) = (x + 7)² - 8
the equation of a quadratic in vertex form is
y = a(x - h)² + k
where (h, k ) are the coordinates of the vertex and a is a multiplier
given the quadratic in standard form : y = ax² + bx + c ( a ≠ 0 )
then the x-coordinate of the vertex is
[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]
f(x) = x² + 14x + 41 is in standard form
with a = 1, b = 14 and c = 41
[tex]x_{vertex}[/tex] = - [tex]\frac{14}{2}[/tex] = - 7
substitute this value into the equation for y- coordinate
y = (- 7 )² + 14(- 7 ) + 41 = 49 - 98 + 41 = - 8
f(x) = (x + 7)² - 8 ← in vertex form
