write the equation x=3y^2-24y+3 in standard form?

Question

Write the equation x =3y^2-24y+3 in standarrd form ?

Answer 1

Given equation is x = 3y^2-24y+3

Standard form of horizontal parabola x = ay^2+by +c

a = 3, b = -24, c = 3

Given equation is belongs to horizontal parabola conic section.

Now to find vertex form.

x = a(y-k)^2 +h

x = 3y^2-24y+3

Add 48 to each side.

x+48 = 3y^2-24y+48+3

x+48 = 3(y^2-8y+16)+3

Subtract 48 from each side.

x+48-48  = 3(y-4)^2+3-48

x = 3(y-4)^2+(-46)

(h,k) = (4,-46).

Comments

The equation in vertex form is x = 3(y - 4)^2 - 45

and vertex of parabola is (h ,k ) = (- 45, 4).