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二次函数
我们能从二次函数的变化中观察到哪些规律？
1. Introduction
Introduction
2. Properties of Quadratic Functions
Properties of Quadratic Functions
3. Average rates on the water balloon tablet
For q(t) = -5t^2 + 20t + 25 the values are q(1) = 40, q(2) = 45, q(3) = 40, q(4) = 25, q(5) = 0. What are the average rates on [1,2], [2,3], [3,4], [4,5]?
4. Effect of the parameter a
In q(x) = ax^2 + bx + c, how does changing a affect the graph?
5. Effect of the parameter c
In q(x) = ax^2 + bx + c, which parameter has the simplest effect, and what is that effect?
6. Quadratic through three points
A quadratic passes through (0, 8), (1, 12) and (2, 12). What is the coefficient a in q(x) = ax^2 + bx + 8?
7. Vertex of a quadratic in standard form
For q(x) = 0.25x^2 - x + 3.5, what is the x-coordinate of the vertex?
8. How many quadratics fit three points
How many quadratic functions have x-intercepts at (-5, 0) and (10, 0) and a y-intercept at (0, -1)?
9. Intercepts from vertex and direction
A quadratic has vertex (-3, -4) and opens upward. What can you guarantee, and what happens if q(-1) = -3 is also known?
10. Intercepts of a downward parabola
How many x-intercepts does p(x) = -3(x+1)^2 + 9 have, and where are they?
11. A parabola with no real intercepts
How many x-intercepts does w(x) = -2x^2 + 10x - 20 have?
12. Three points fix a quadratic when the vertex is one of them
A quadratic with an upward opening and a vertex below the x-axis can have at least one x-intercept, but the vertex alone never fixes its formula.