How do you find the axis of symmetry, and the maximum or minimum value of the function #y = 3x^2 + 24x - 1#?

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Answer 1 · 2016-05-30T20:42:15

#3x^2+24x-1 equiv 3(x+4)^2-49#

Giving a parabola written as

#y = a(x-x_0)^2+b#

geometrically speaking we can qualify:

#{(x_0 = "axis of symmetry"), (a = "scale factor"), (b = "offset value"):}#

Given a parabola such as

#y = 3x^2+24x-1#

we can reduce it to the former formulation, making

#3x^2+24x-1 = a(x-x_0)^2+b#

and equating the coefficients, results in

#{(-1 - b - a x_0^2 = 0), (24 + 2 a x_0=0), (3 - a=0):}#

solving for #a,b,x_0#

#{a = 3, b = -49, x_0 = -4}#

and the equivalent formulation

#3x^2+24x-1 equiv 3(x+4)^2-49#