Problem:

Find the equation of the parabola with vertex at the origin, its axis along the x axis, and passes through the point (-3,6). Graph the parabola​.

Solution:

vertex at origin

vertex V(0, 0), horizontal axis, through (-3,6)​

h = 0, ; k = 0

x = a(y - k)² + h

x = a(y - 0)² + 0

if x = -3 ; y = 6

-3 = a(6 - 0)² + 0

-3 = a(6²)

-3 = 36a

a = -3/36

a = -1/12

x = a(y - 0)² + 0

x = -1/12(y²)

12x = -y²

y² = -12x

y² = -12x

4a = -12

a = -3

focus (a, 0)

focus (-3, 0)

Answer:

Equation of parabola:

y² = -12x

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