MHF 4U1
1.
NAME:_______________________________
Solve the following systems of equations by ELIMINATION.
a)
7a  b  2
3a  2b  3
b)
3 x  4  4 y
7 x  6 y  11
c)
x

2
x

3
y
4
8
y
 2
2
d)
3
f 
4
2.
3
Given f ( x)  2 x  5x  3 , evaluate
3.
Write the domain and the range of each function. Graph each function.
a) f ( x)  4 x  2
b) f ( x)  2( x  1) 2  4
c) f ( x)  x 3
d) f ( x ) 
4.
x
5
2

x3 x
b)
1
x

x  2 x 1
c)
x 2  3x  18
9  x2
Solve for x, then formally check your solution. No decimals!
a)
6.
e) f  x  
b)
f (2)
Simplify each expression.
a)
5.
1
x4
a)
0.4 x  0.2 y  0.5
x  0.5 y  0.1
3(2 x  1)  3  2( x  6)
b)
3x  1 x  1

5
4
c)
Solve for x by factoring. No decimals (and no quadratic formula)!
a) 4 x 2  x  3  0
b) 9 x 2  15  48 x c) 21x 2  1  10 x
d) x 2  4 x  32  0
e) x 2  6 x  5  0
f) 2 x 2  9 x  0
x  3 2x  5

 3
2
5
g) 6 x 2  31x  5  0
7.
Determine both the x and y-intercepts for each of the following functions.
Express your answers in exact form.
a) 9 x  5 y  18  0
b) y  2 x 2  8 x  1 c) y  5 x 2  2 x  8 d) y   x 2  2 x  7
8.
Use the quadratic formula to solve. Round to 1 decimal place.
a) 2 x 2  7 x  4  0
b) 7 x  20  6 x 2
c)
2 x 2  5 x  12  0
9.
Determine an equation for the quadratic function, with the given zeros, and that passes
through the given point.
a)
zeros: -4 and 1; point (-1, 2)
b)
zeros: -3 and 4; point (3, 24)
c)
zeros: 5 and -1; point (4, -10)
d)
zeros: 3/2 and -1/2; point (0, 9)
10.
For each of the following functions, write in vertex form and sketch. Label vertex, axis of
symmetry, and two symmetrical points.
a)
b)
y  2 x 2  20 x  44
y  3x 2  6 x  2
Answers
1
15
,b  
11
11
1.
a) a 
2.
a) -3
3.
a) x  Ry  R
1
2
b) x  2, y 
b)

3x  6
x( x  3)
b)
5.
a) x  3
b)
6.
a)  1,
3
4
b)



x 2  3x  1
( x  2)( x  1)
x
c)
9
7
c)
c)
1 1
,
7 3
g) -5, 
d) 8, -4
1
6
8.
a) x  0.7 or x  2.8
b) x  1.3 or x  2.5
9.
a) y   ( x  4)( x  1)
1
3
c) y  2( x  1)( x  5)
b) y  4( x  3)( x  4)
10.
a)
b)

x  5
c) no x-intercepts ; y  8
a) x  2, y  
x  Ry  R
c)
 ( x  6)
x3
 4  14
, y 1
2
d) x  1  2 2 , y  7
7.
no solution
e) x  R x  0 y  R y  0
1
,5
3
9
f) 0,
2
e) -5, -1

b) x  R y  R y  4

a)
d)
x  6, y  8
3
32
d) x  R, x  4 y  R y  0
4.
c)
18
5
b) x 
d) y  3(2 x  1)( 2 x  3)
y  2( x  5) 2  6 ; vertex (5,6) ; axis of symmetry x  5 ; points (4, 4) & (6, 4)
y  3( x  1) 2  1 ; vertex (-1, 1) ; axis of symmetry x  1 ; points (-2, -2) & (0, -2)
a)
b)
10
10
8
8
6
6
4
4
2
2
-10 -8 -6 -4 -2
2
-2
-4
-6
-8
-10
4
6
8 10
-10 -8 -6 -4 -2
2
-2
-4
-6
-8
-10
4
6
8 10