What is the vertices 5x(2x+4)-3x ?

The vertices 5x(2x+4)-3x is Minimum (-17/20 ,-289/40)

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vertices 5x(2x+4)-3x

vertices

5 x (2 x + 4) - 3 x

Minimum (- \frac{17}{20}, - \frac{289}{40})

Solution steps

y = 5 x (2 x + 4) - 3 x

Rewrite

y = 5 x (2 x + 4) - 3 x

in the form

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

y = 10 x^{2} + 17 x

The parabola parameters are:

a = 10, b = 17, c = 0

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

x_{v} = - \frac{17}{2 \cdot 10}

Simplify

x_{v} = - \frac{17}{20}

Plug in

x_{v} = - \frac{17}{20}

to find the

y_{v}

value

y_{v} = - \frac{289}{40}

Therefore the parabola vertex is

(- \frac{17}{20}, - \frac{289}{40})

a < 0,

then the vertex is a maximum value

a > 0,

then the vertex is a minimum value

a = 10

Minimum (- \frac{17}{20}, - \frac{289}{40})

f (x) = - 4 x^{2} - 12 x + 5

f (x) = 3 x^{2} - x + 1

y = - 2 x^{2} + 5

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

- 2.318 + 0.2356 x - 0.002674 x^{2}

What is the vertices 5x(2x+4)-3x ?
The vertices 5x(2x+4)-3x is Minimum (-17/20 ,-289/40)