What is the vertices x^2=20y ?

The vertices x^2=20y is Minimum (0,0)

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vertices x^2=20y

vertices

x^{2} = 20 y

Minimum (0, 0)

Solution steps

x^{2} = 20 y

Rewrite

x^{2} = 20 y

in the form

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

y = \frac{1 \cdot x ^{2}}{20}

The parabola parameters are:

a = \frac{1}{20}, b = 0, c = 0

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

x_{v} = - \frac{0}{2 ( \frac{1}{20} )}

Simplify

x_{v} = 0

Plug in

x_{v} = 0

to find the

y_{v}

value

y_{v} = 0

Therefore the parabola vertex is

(0, 0)

a < 0,

then the vertex is a maximum value

a > 0,

then the vertex is a minimum value

a = \frac{1}{20}

Minimum (0, 0)

y^{2} = 16 x

y^{2} = - 24 x

9 x^{2} - 16 y^{2} + 36 x + 32 y - 124 = 0

4 x^{2} + 4 y^{2} + 36 y + 5 = 0

x^{2} + \frac{y ^{2}}{64} = 1