What is the vertices y=84x-x^2 ?

The vertices y=84x-x^2 is Maximum (42,1764)

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vertices y=84x-x^2

vertices

y = 84 x - x^{2}

Maximum (42, 1764)

Solution steps

y = 84 x - x^{2}

Rewrite

y = 84 x - x^{2}

in the form

y = a x^{2} + b x + c

y = - x^{2} + 84 x

The parabola parameters are:

a = - 1, b = 84, c = 0

x_{v} = - \frac{b}{2 a}

x_{v} = - \frac{84}{2 ( - 1 )}

Simplify

- \frac{84}{2 ( - 1 )} : 42

x_{v} = 42

Plug in

x_{v} = 42

to find the

y_{v}

value

y_{v} = 1764

Therefore the parabola vertex is

(42, 1764)

a < 0,

then the vertex is a maximum value

a > 0,

then the vertex is a minimum value

a = - 1

Maximum (42, 1764)

\frac{x ^{2} x ^{1}}{x}

y = x^{2} - 2 x

f (x) = 3 x^{2} + 6 x + 4

f (x) = 5 x^{2}

f (x) = x^{2} - 6 x + 9