Practice Quiz 10-1
Name____________________
1. Find the standard equation of the parabola with the given characteristics and vertex at
the origin: Focus: (0, 3).
2. Find the focus of the parabola x= 3(y2+2y+33)
3. Find the Standard Form of the equation of the parabola with the given characteristics
A. Vertex (6,3); focus (2,3)
B. Vertex (2,4); directrix: y = 7
Explanations
1. X2=4py or y2=4px
X2=4py
X2=4(3)y
X2=12y
2. x=3(y2+2y+33)
x/3=y2+2y+33
1+(x/3 -33)=(y2+2y)+1
x/3 -32=y2+2y+1
1/3(x -96)=(y+1)2
P=1/12, h=96, k=-1
Focus=(-11/12, 96)
3.
a. (y – 3)2 = -16(x – 6)
(x – 2)2 = -12(y – 4)
The standard form of a parabola can be
represented by the two different
equations, either y2=4px for the horizontal
axis, or x2=4py for the vertical axis.
Because the origin is the vertex and the
focus is (0, 3), we know that the parabola
opens upward and therefore the axis of the
parabola is vertical. Because of this, we
use the vertical axis equation, (x2=4py).
The variable P is the distance from the
vertex of the parabola to the focus point.
The distance from 0 to 3 on the y axis is 3
in this equation, so I plug in a 3 for P. This
gives me the following equation: x2=4(3) y.
I multiply the 4 and 3 and get x2=12y. This
is the standard equation for the parabola
with its vertex at the origin and a focus
point of (0, 3).
To get the y2 value alone, you divide both
sides by 3. Complete the square by
subtracting 33 from both sides, taking half
of the 2y value, squaring that value and
adding it to both sides. Take out 1/3 out of
the parentheses so x is left alone and factor
y2+2y+1. Use the equation for a parabola
pointed to the right (y – k)2 4p(x – h) and
use the p, h, and k to find the focus using
(h+p, k)
Simply plug into the standard equation of a
parabola.