What is the vertices f(x)=2x^2+3x-4 ?

The vertices f(x)=2x^2+3x-4 is Minimum (-3/4 ,-41/8)

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vertices f(x)=2x^2+3x-4

vertices

f (x) = 2 x^{2} + 3 x - 4

Minimum (- \frac{3}{4}, - \frac{41}{8})

Solution steps

y = 2 x^{2} + 3 x - 4

The parabola parameters are:

a = 2, b = 3, c = - 4

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

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

Simplify

x_{v} = - \frac{3}{4}

Plug in

x_{v} = - \frac{3}{4}

to find the

y_{v}

value

y_{v} = - \frac{41}{8}

Therefore the parabola vertex is

(- \frac{3}{4}, - \frac{41}{8})

a < 0,

then the vertex is a maximum value

a > 0,

then the vertex is a minimum value

a = 2

Minimum (- \frac{3}{4}, - \frac{41}{8})

y = 5 x^{2} - 2 x - 1

f (x) = x^{2} - 10 x + 21

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

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

(x - 1)^{2} = - 4 (y - 2)

What is the vertices f(x)=2x^2+3x-4 ?
The vertices f(x)=2x^2+3x-4 is Minimum (-3/4 ,-41/8)