I need the answer to this question Please show all work You

I need the answer to this question. Please show all work. You must write the equation in standard form. Please type answer, don\'t write on paper. Thanks!!!

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What is the equation of a parabola with a vertex at (0, 0) and a focus at (0, 6)

Solution

Vertex: (h, k) = (0,0) => h=0, k=0

Focus: (h, k+(1/4a)) = (0,6) => a = 1/24

Vertex form of parabola equation => y = a(x-h)² + k

Standard form of parabola equation => y = ax² + bx + c

On comparing above two,

c = ah² + k = a*(0)² + 0 = 0;

b = -2ah = -2(1/24)(0) = 0

Putting values in standard form of parabola we get, y = ax² and a = 1/24

=> y = (1/24)x² is the equation of the parabola.