What is the vertices (r-14)^2-56.25 ?

The vertices (r-14)^2-56.25 is Minimum (14,-56.25)

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vertices (r-14)^2-56.25

vertices

(r - 14)^{2} - 56.25

Minimum (14, - 56.25)

Solution steps

y = (r - 14)^{2} - 56.25

Rewrite

y = (r - 14)^{2} - 56.25

in the form

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

y = r^{2} - 28 r + 139.75

The parabola parameters are:

a = 1, b = - 28, c = 139.75

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

r_{v} = - \frac{( - 28 )}{2 \cdot 1}

Simplify

r_{v} = 14

Plug in

r_{v} = 14

to find the

y_{v}

value

y_{v} = - 56.25

Therefore the parabola vertex is

(14, - 56.25)

a < 0,

then the vertex is a maximum value

a > 0,

then the vertex is a minimum value

a = 1

Minimum (14, - 56.25)

y = 7 - 6 x^{2}

y = 2 x^{2} - 1 + 5 x - 6

f (x) = - \frac{5}{8} x^{2} + \frac{1}{4} x - 2

f (x) = - 16 x^{2} + 4 x + 10

y = (x + 1)^{2}

What is the vertices (r-14)^2-56.25 ?
The vertices (r-14)^2-56.25 is Minimum (14,-56.25)