Algebra 2
5.1 day 1 worksheet
Mathematician _____________________________ P. ____
For the following functions:
(a) tell whether the graph opens up or opens down,
(b) find the axis of symmetry
(c) find the vertex
(d) find the y-intercept
(e) graph the function.
1.
y = x2 + 1
opens: UP or DOWN
axis of sym: __________
vertex: ___________
y-intercept: __________
2. f(x) = –x2 + 4
opens: UP or DOWN
axis of sym: __________
vertex: ___________
y-intercept: __________
3. y = x2 + 4x + 3
opens: UP or DOWN
axis of sym: __________
vertex: ___________
y-intercept: __________
4. f(x) = 4x2 + 8x + 1
opens: UP or DOWN
axis of sym: __________
vertex: ___________
y-intercept: __________
5. f(x) = -x2 + 4x – 2
opens: UP or DOWN
axis of sym: __________
vertex: ___________
y-intercept: __________
3
6. y = - x2 + 3
2
opens: UP or DOWN
axis of sym: __________
vertex: ___________
y-intercept: __________
Tell whether the function has a minimum value or a maximum value. Then find the minimum or maximum value.
7. y = -6x2 – 1
8. y = 9x2 + 7
9. f(x) = 2x2 + 8x + 7
1
10. g(x) = - x2 - 8x + 2
2
11. The path that a motocross dirt bike rider follows during a jump is given by y = -0.4x2 + 4x + 10 where x is the
horizontal distance (in feet) from the edge of the ramp and y is the height (in feet). What is the maximum
height of the rider during the jump?
12. Multiple choice. What is the effect on the graph of the function y = x2 + 2 when it is changed to y = x2 – 3?
A. the graph widens
B. the graph narrows
C. the graph opens down
D. the vertex moves down the y-axis
13. Multiple choice. Which function has the widest graph? Explain how you know.
A. y = 2x2
B. y = x2
C. y = 0.5x2
D. y = -x2