Algebra II A.93 HonorsTest PracticeMonday, February 25
TEST is TUESDAY, FEB 26
1) Match each Standard Form equation to the conic section it represents:
a) P1b) C1 c) E1
d) E2e) H1 f) H2
C1. circle with center (h, k) and radius r
E1. ellipse with center (h, k) and a horizontal major axis
E2. ellipse with center (h, k) and a vertical major axis
P1. parabola with vertex (h, k)and axis of symmetry x = h
H1. horizontal hyperbola with center (h,k)
H2. vertical hyperbola with center (h,k)
Parabolas- Find the vertex and axis of symmetry for each and graph (use 5 accurate points):
2) 3)
Vertex _______Vertex _______
Axis of symmetry _x=0 (y-axis)______Axis of symmetry _______
See graphs at end of documentSee graphs at end of document
LOOK CAREFULLY AT SCALES FOR EACH GRAPH!
4) dotted line, shade inside curve5) solid line, shade outside
Vertex _______Vertex _______(below) curve
Axis of symmetry _______Axis of symmetry _______
See graphs at end of documentSee graphs at end of document
Change each to standard form by completing the square; then state its vertex and axis of symmetry.
6) 7) 8)
Distance and Midpoint:
9) Distance is always a _positive__ number.10) Give the distance formula:
Find the distance between each of the following points:
11)
12)
13)
Find the midpoint between each of the following points:
14)
15)
16)
Circles: find the center and radius for each and graph:
17) 18)
Center _______Center _______
Radius ___5____Radius ___2____
See graphs at end of documentSee graphs at end of document
Change each to standard form by completing the square; then state its center and radius.
19) 20)
Ellipses:
21) 22)
horizontal or vertical?horizontal or vertical?
center _________center ________
length of major axis __10_____length of major axis __10_____
length of minor axis ____8___length of minor axis ____6___
_____ ______
foci foci __
Graph:Graph:
Endpoints of major axis: (4, -2)(-6, -2)Endpoints of major axis: (-3, 6)(-3, -4)
Endpoints of minor axis (-1, 2)(-1, -6)Endpoints of minor axis (-6, 1)(0, 1)
Center (-1, -2) Center (-3, 1)
Foci: (2, -2) & (-4, -2)Foci: (-3, 5) & (-3, -3)
Hyperbolas:
23) 24)
horizontal or vertical?horizontal or vertical?
center _________center ________
foci foci
Graph:Graph:
Mixture of Writing Equations: (use the graphs to help if necessary)
25) Write an equation for a parabola with vertex that is of “normal” size and opens down.
26) Write an equation for a parabola that is very narrow, opens up, shifted right 3 and up 5.
27) Write an equation for a circle with center at the origin and a radius of .
28) Write an equation for a circle with center and radius = 4.
29) Write an equation of a circle tangent to the y-axis with center (6, 5).
30) Write an equation of an ellipse with center at , length of minor axis is 6, and foci at .
31) Write an equation of an ellipse whose major axis has
endpoints and whose foci are .
32) Change to standard form and identify the type of conic section:
33) Write an equation of a vertical hyperbola with center at , vertices at ,
and the slope of the asymptotes =
34) Write an equation of a hyperbola with vertices at and whose foci are .
35) Solve these systems:
(Unusual things might
happen)
No Solution
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