What is the directrix of the parabola with the equation y+3= 1/10 (x+2)^2?
What you have to know about parabolas in standard form:
1: Parabolas whose equations are in the standard form
opens upward if and downward if
They have vertex (h, k), focus (h, k+p), and
the directrix is the horizontal line whose equation
is y=k-p
2: Parabolas whose equations are in the standard form
opens rightward if and leftward if
They have vertex (h, k), focus (h+p, k), and
the directrix is the vertical line whose equation
is x=h-p.
Your equation
can be placed in the standard form 1.
Multiply both sides by 10
Swap sides:
Compare to the standard equation in 1 above:
So so ,
so
so
opens upward because
It has vertex (h, k) = (-2,-3)
It has focus (h, k+p) = (-2,-3+) = (-2, )
the directrix is the horizontal line whose equation
is or or
To draw the graph, plot the focus (-2, ), the vertex(-2,-3) and
the directrix
Draw a line from the focus directly to the directrix. The
vertex should be the midpoint of this line.
Draw a square with that line being its left side:
Draw another square with that line being its right side:
Finally, draw the parabola through the vertex and the
upper corners of the two squares:
Edwin