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Lesson: 2.5 一元二次函数的极值 The Extreme Values of Quadratic Functions
2.5 The Extreme Values of Quadratic Functions 一元二次函数的极值
[1]

Given that beside is the graph of the curve whose equation is y = p– (x–q), find

(a) the values of p and q
p 和 q 的值，

(b) the maximum value of y.
y 的最大值

(a) 1, 2

(b) 1

[2]

Given that 2x + ax + b has a minimum value 3 when x = 2. Find the values of a and b.

-8, 11
[3]

Find the minimum or maximum value of 9 + 5x – 3x and state where it occurs.

, when当 x=

[4]

The diagram shows the graph of the function y = (x – k) + 2, where k is a constant. Find

(a) the value of k,
k的值，

(b) the equation of the axis of symmetry,

(c) the coordinate of the minimum point.

(a) 3

(b) x = 3

(c) (3, 2)

[5]

If y = 2x + 5x + 4, find the range of

[6]

If the sum of two numbers is 18, find the minimum value of the sum of their square.

162
[7]

The function g(x) = + 4hx – 5h– 1 has a maximum value of –k – 2h, where h and k are constants.

(a) By completing the square, show that k = h – 1.

(b) Hence, find the value of h and k if the graph of the function g(x) is symmetrical about x = k – 1, such that h 0.

(b) 4, 3

[8]

Given that f (x) = x – qx – x – 3 and g(x) = -2x + 4x + 3p, and they meet at x axis

(a) find the values of p and q,

(b) the minimum value of f (x),
f (x)的最小值，

(c) the maximum value of g(x).
g(x)的最大值。

(a) 2, 1

(b) –4

(c) 8

[9]

Find the range of values taken by for all values of x.

(0, ]
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