What is the vertices (x+4)^2 ?

The vertices (x+4)^2 is Minimum (-4,0)

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vertices (x+4)^2

vertices

(x + 4)^{2}

Minimum (- 4, 0)

Solution steps

y = (x + 4)^{2}

y = (x + 4)^{2}

The parabola parameters are:

a = 1, m = - 4, n = - 4

x_{v} = \frac{m + n}{2}

x_{v} = \frac{( - 4 ) + ( - 4 )}{2}

Simplify

x_{v} = - 4

Plug in

x_{v} = - 4

to find the

y_{v}

value

y_{v} = 0

Therefore the parabola vertex is

(- 4, 0)

a < 0,

then the vertex is a maximum value

a > 0,

then the vertex is a minimum value

a = 1

Minimum (- 4, 0)

f (x) = x^{2} - 6 x - 7

x^{2} - 2 x - 8

x^{2} - 6 x + 10

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

f (x) = x^{2} + 10 x + 9