Question

Find the vertex form for the following quadratic function. f(x)=x^2+14x+41

Answer 1

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

$x_{vertex}$ = - $\frac{b}{2a}$

f(x) = x² + 14x + 41 is in standard form

with a = 1, b = 14 and c = 41

$x_{vertex}$ = - $\frac{14}{2}$ = - 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