Algebra II Pre AP
Worksheet 4.1, 4.2, 4.7, 4.8, 4.10
Name:_____________________
1. A parabola represented by an equation y  ax 2  bx  c is given. Study each graph and then tell
whether the value of each expression that follows is positive, negative, or zero.
a. b 2  4ac
b. b 2  4ac
_______
a ____ b____ c____
c. b 2  4ac
_______
a ____ b____ c____
_______
a ____ b____ c____
2. Tell how many times the parabola y  x 2  6 x  10 intersects each of the following:
a. the y-axis _______
b. the line y = 1 _______
c. the line y = 2 ______
3. Write an equation in vertex form for each parabola described below.
a. the vertex is (4, -3); the parabola contains the point (2, -1)
____________________________
b. the vertex is at the origin; the graph contains (-3, 3)
____________________________
c. the vertex is (3, 5); the y-intercept is (0, 2)
____________________________
d. the vertex is (4, 2); an x-intercept is (3, 0)
____________________________
4. If the parabola y  8  3  x  h  has the line x  5 as its axis of symmetry, find h.
__________
5. If the parabola y  3  a  x  1 passes through the point (2, 5), find a.
__________
2
2
6. Find values of a and k for which each parabola contains the given points.
a. y  k  a  x  1 ; (3, 11) and (1, 3)
2
a  _________
k  _________
b. y  k  a  x  3 ; (-5, 1) and (1, 7)
a  _________
k  _________
2
7. Complete the square and write the equation in vertex form, then state the vertex.
equation in vertex form
vertex
____________________
___________ a. f ( x)  5  2 x  x 2
____________________
___________ b. f ( x)  3x 2  12 x
____________________
___________ c. g ( x)  2 x 2  12 x  18
8. Use the formula
vertex
b
to find the vertex for each of the following, then write the equation in vertex form.
2a
equation in vertex form
___________
____________________ a. h( x)  6  6 x  x 2
___________
____________________ b. g ( x) 
1 2
1
x x
2
2
___________
____________________ c. h( x) 
1 2
5
x  2x 
4
2
9. Average the roots to find h . State the vertex and use the vertex and roots to graph each function.
a. h( x)   2 x  5 2 x  3 vertex _________
b. f ( x)   2  x  5  x 
c. h( x)  2  x  7  x  5
d. g ( x) 
vertex _________
vertex _________
1
 6  x  4  x  vertex _________
2