What is the vertices 2x(x-9)-(x-9) ?

The vertices 2x(x-9)-(x-9) is Minimum (19/4 ,-289/8)

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vertices 2x(x-9)-(x-9)

vertices

2 x (x - 9) - (x - 9)

Minimum (\frac{19}{4}, - \frac{289}{8})

Solution steps

y = 2 x (x - 9) - (x - 9)

Rewrite

y = 2 x (x - 9) - (x - 9)

in the form

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

y = 2 x^{2} - 19 x + 9

The parabola parameters are:

a = 2, b = - 19, c = 9

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

x_{v} = - \frac{( - 19 )}{2 \cdot 2}

Simplify

x_{v} = \frac{19}{4}

Plug in

x_{v} = \frac{19}{4}

to find the

y_{v}

value

y_{v} = - \frac{289}{8}

Therefore the parabola vertex is

(\frac{19}{4}, - \frac{289}{8})

a < 0,

then the vertex is a maximum value

a > 0,

then the vertex is a minimum value

a = 2

Minimum (\frac{19}{4}, - \frac{289}{8})

y = x^{2} + 2 x + 4

y = x^{2} + 2 x + 5

y = - 2 x^{2} - 4 x - 7

f (x) = x^{2} - 12 x

f (x) = x^{2} + 4 x - 21

What is the vertices 2x(x-9)-(x-9) ?
The vertices 2x(x-9)-(x-9) is Minimum (19/4 ,-289/8)