The document compares the graphs of the quadratic functions f(x) = x^2 and f(x) = -x^2. Both functions have a parabola shape that is symmetric around the y-axis. However, f(x) = x^2 opens upward, while f(x) = -x^2 opens downward due to the negative coefficient changing the direction of the opening of the parabola. In general, the properties of quadratic functions with an equation of y = ax^2 are also described.

1. On the same graph
Graph f(x) = x 2 Graph f(x) = ­ x2

3. y = x2 y = ­x2

5. y =
1
y =

7. In general the following statements are true for each
quadratic function of the type y = ax2:
1. Axis of symmetry is the y­axis, its equation is x = 0.
2. Coordinates of the vertex are (0, 0).
3. If graph opens upward.
If , graph opens downward
4. If , graph is narrower than y = x2 (stretch)
If , graph is wider than y = x2 (shrunk)
5. If a > 0, the minimum value of y is 0.
If a < 0, the maximum value of y is 0.

8. Exercise 2
Omit #9, and #10