What is the vertices-2x+x(x-2)-2x(x-1)-(x-3) ?

The vertices-2x+x(x-2)-2x(x-1)-(x-3) is Maximum (-3/2 , 21/4)

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vertices-2x+x(x-2)-2x(x-1)-(x-3)

vertices

- 2 x + x (x - 2) - 2 x (x - 1) - (x - 3)

Maximum (- \frac{3}{2}, \frac{21}{4})

Solution steps

y = - 2 x + x (x - 2) - 2 x (x - 1) - (x - 3)

Rewrite

y = - 2 x + x (x - 2) - 2 x (x - 1) - (x - 3)

in the form

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

y = - x^{2} - 3 x + 3

The parabola parameters are:

a = - 1, b = - 3, c = 3

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

x_{v} = - \frac{( - 3 )}{2 ( - 1 )}

Simplify

x_{v} = - \frac{3}{2}

Plug in

x_{v} = - \frac{3}{2}

to find the

y_{v}

value

y_{v} = \frac{21}{4}

Therefore the parabola vertex is

(- \frac{3}{2}, \frac{21}{4})

a < 0,

then the vertex is a maximum value

a > 0,

then the vertex is a minimum value

a = - 1

Maximum (- \frac{3}{2}, \frac{21}{4})

(5 x - 8)^{2}

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

- x^{2} + 7

- x^{2} - 4

f (x) = - (x - 3)^{2} + 2

What is the vertices-2x+x(x-2)-2x(x-1)-(x-3) ?
The vertices-2x+x(x-2)-2x(x-1)-(x-3) is Maximum (-3/2 , 21/4)