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

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

= -

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

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

= - = - 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

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