What is the vertices y=2x^2-6x ?

The vertices y=2x^2-6x is Minimum (3/2 ,-9/2)

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vertices y=2x^2-6x

vertices

y = 2 x^{2} - 6 x

Minimum (\frac{3}{2}, - \frac{9}{2})

Solution steps

y = 2 x^{2} - 6 x

The parabola parameters are:

a = 2, b = - 6, c = 0

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

x_{v} = - \frac{( - 6 )}{2 \cdot 2}

Simplify

- \frac{- 6}{2 \cdot 2} : \frac{3}{2}

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

Plug in

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

to find the

y_{v}

value

y_{v} = - \frac{9}{2}

Therefore the parabola vertex is

(\frac{3}{2}, - \frac{9}{2})

a < 0,

then the vertex is a maximum value

a > 0,

then the vertex is a minimum value

a = 2

Minimum (\frac{3}{2}, - \frac{9}{2})

f (x) = - \frac{1}{3} x^{2} - \frac{7}{6} x + 1

4 x^{2} + 4 x - 8

f (x) = - 2 x^{2} - 16 x - 31

- x^{2} + 2 x + 2

f (x) = - 2 x^{2} - 16 x - 37