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Date: _______
Date: ______________________________
Algebra 2 - Chapter 10 Practice Test
1.
Determine the midpoint for each of the following pair of points
a)
( 14 , 9 ) ( 2 , 21 )
b)
( –8 , 8 ) ( 8 , –4 )
c)


2.
Determine the distance between the following pair of points
a)
( –4 , 7 ) ( 2 , –1 )
b)
( –12 , 8 ) ( –8 , 2 )

3.
Write the following quadratic equation in vertex form. Using this converted form,
determine the vertex.
Y = X2 + 8X + 25
1
4.
Write the following quadratic equation in vertex form. Using this converted form,
determine the vertex.
2Y + 4X2 – 8X + 24 = 0
5. For the parabola equation
the formula for the focus is
2
x = a(y – k) + h
(h+
,k)
What is the focus for the following parabola?
x = 2 – 2(y + 3)2
6. A circle has center = ( –8 , 8 ) and its radius = 4
Write the standard equation for this circle
7. For the following circle, determine the center and the radius
(x + 4)2 + (y – 3)2 = 10
Center =
Radius =
2
8.
These questions have 2 parts: (1) Find the vertex, axis of symmetry, focus, directrix for each equation. (2)
Graph each function on the coordinate grid below. Label each graph by putting the function’s letter by its
vertex.
A)
y =
B)
y = 2
C)
y = 5 –
–4
–9
3
9. Sketch the following circles on the coordinate chart.
(x – 5)2 + (y – 4)2 = 4
(x + 4)2 + (y – 3)2 = 1
(y + 4)2 + (x – 2)2 = 9
10. Write out the equations for each of the circles shown below. For each circle, you must
show your work. To do this … find the center and radius and then use this information to
write the equation for the circle.
Circle A:
Center =
Radius =
Equation:
Circle B:
Center =
Radius =
Equation:
Circle C:
Center =
Radius =
Equation:
4
11. Graph each equation and give the domain and range:
(A)
(B)
(C)
5
ANSWERS
1.
a) ( 8 , 15 )
b) ( 0 , 2 )
2.
a) 10
b)
3.
Y = (X + 4)2 + 9
4.
Y = –2(X – 1)2 – 10
c)
=
= 2
Vertex = ( –4 , 9 )
Vertex = ( 1 , –10 )
5.
6.
(X + 8)2 + (Y – 8)2 = 16
7.
Center = ( –4 , 3 ) Radius =
8. (A) Vertex
; Focus:
Directrix:
; Graph faces up from vertex
(B) Vertex
; Axis of symmetry:
Directrix:
; Graph faces up from vertex
(C) Vertex
; Axis of symmetry:
Directrix:
9.
; Axis of symmetry:
;
.
; Focus:
;
.
; Focus:
; Graph faces down from vertex
;
.
Sketch of circles
10. Circle A: Center = ( –1 , 4 ); Radius = 3; Equation: (X + 1)2 + (Y – 4)2 = 9
Circle B: Center = ( –5 , –1); Radius = 2; Equation: (X + 5)2 + (Y + 1)2 = 4
Circle C: Center =
; Radius = ; Equation: (X – )2 + (Y + 4)2 =
11. (A) An ellipse with center (0,0); Domain:
; Range:
(B) A hyperbola, opens horizontally, center (0,0); Domain:
numbers. (C) A circle with center (2,-3), radius =5; Domain:
; Range: all real
; Range:
6