Quadratic function f (x) = 2x Λ 2 + 2x + 3, find f (0), f (2) and find the maximum value of F (x)

Quadratic function f (x) = 2x Λ 2 + 2x + 3, find f (0), f (2) and find the maximum value of F (x)

f(x) = 2x^2+2x+3
= 2(x+1/2)^2 + 5/2
f(0) = 3
f(2) = 15
no max

Find the maximum value of the function f (x) = x ^ 2-2x-3 where x belongs to [T, t + 2]

The function f (x) = x ^ 2-2x-3, the opening of the image is upward, and the axis of symmetry is x = 1,
When the interval [T, t + 2] is on the left side of the symmetry axis, that is, t + 2

Given the function AF (x) + BF (- x) = CX, (absolute value a is not equal to absolute value b), find the analytic expression of F (x)

The absolute value a is not equal to the absolute value B
A ± B ≠ 0
af(x)+bf(-x)=cx ①
af(-x)+bf(x)=c-x ②
① (a + b) (f (x) + F (- x)) = 0
∴f(x)+f(-x)=0
That is, f (- x) = - f (x)
The original formula is changed to AF (x) - BF (x) = Cx
∴f(x)=cx/(a-b)

Simple calculation of 5 / 12 + (7 / 9 + 7 / 12)

First calculate (7 / 9 + 7 / 12) = 21 / 7 = 3 = 15 / 5, then add 5 / 12, that is 12 / 5 + 15 / 5 = 27 / 5

What is the range of y = - (lgx) ^ 2?
Whether the value range of y = - (lgx) ^ 2 is (- ∞, 0], and the definition field is (0, + ∞)

Yes, your answer is right

A square with a side length of 4cm has the same perimeter and area______ (judge right or wrong)

The perimeter is 4 × 4 = 16 (CM); the area is 4 × 4 = 16 (cm 2); the value of perimeter and area is the same, but the units are not the same, and the length unit and area unit cannot be compared

4.4.10.10. How to calculate the final equal to 24

1:(10 × 10 - 4) ÷ 4
2:((10 × 10) - 4) ÷ 4

In known sequence {an}, an > 0, s = a1 + A2 +. + an, and an = 6sn / (an + 3), find SN

This problem is not very difficult. It mainly uses one-step transformation, that is, an = SN-S (n-1),
An = 6sn / (an + 3), that is, (an) ^ 2 + 3an = 6sn, recursion of a term gives [a (n-1)] ^ 2 + 3A (n-1) = 6S (n-1)
Therefore, the key and obvious formula of subtraction between the two formulas is as follows:
[an-a (n-1)] [an + a (n-1)] = 3 [an + a (n-1)], because an > 0, we get an-a (n-1) = 3
That's the arithmetic sequence that you are familiar with. The first item is given by the recursion of the title, which is A1 = 3 (A1 = S1)
So an = 3 + 3 (n-1) = 3N, so Sn = [3N (n-1)] / 2
Sometimes, when you encounter a similar problem, you should immediately think of an = SN-S (n-1). Generally, Sn is used to replace an, and sometimes an is used to replace SN. Depending on the situation, it's much easier to try to convert the recurrence formula into an equal difference or equal ratio sequence

Do you change the perimeter and area of a square into a parallelogram?

Perimeter unchanged, area smaller

How to do math 2-3 + 5-4 + 6 in grade one

2-3+5-4+6=6