What is the vertices f(x)=2x^2-6x+15 ?

The vertices f(x)=2x^2-6x+15 is Minimum (3/2 , 21/2)

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vertices f(x)=2x^2-6x+15

vertices

f (x) = 2 x^{2} - 6 x + 15

Minimum (\frac{3}{2}, \frac{21}{2})

Solution steps

y = 2 x^{2} - 6 x + 15

The parabola parameters are:

a = 2, b = - 6, c = 15

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{21}{2}

Therefore the parabola vertex is

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

f (x) = 2 x^{2} + 5 x - 3

4 (x + \frac{3}{2})^{2} + 15

f (x) = 2 x^{2} - 8 x

x^{2} + 4 x + 4 y - 4 = 0

y^{2} = - 24 x

What is the vertices f(x)=2x^2-6x+15 ?
The vertices f(x)=2x^2-6x+15 is Minimum (3/2 , 21/2)