Question

How do you write the equation in standard form, then determine the vertex, axis and direction in which each parabola opens?

x^2 + 2x - 3y + 19 = 0

Answer 1

write the eq in general form
\[X^2=4aY\]

Answer 2

vertex is X=0 Y=0

Answer 3

\[x^2+2x+1=3y-19+1\]

Answer 4

Standard form is y = ax^2 + bx + c
So add 3y to both sides
x^2 + 2x + 19 = 3y
now divide by 3
y = 1/3 x^2 + 2/3 x + 19/3
It will open up along the y-axis. The vertex is (-1, 6)

Answer 5

\[(x+1)^2=3y+18\]

Answer 6

\[(x+1)^2=3(y+6)\]

Answer 7

so
\[X^2=3Y\]