Finding the maximum or minimum value of quadratic trinomial 2x ^ 2 + 8x

2X^2+8X
=2X^2+8X+8-8
=2(X+2)^2-8
The square is greater than or equal to 0
2(X+2)^2>=0
2(X+2)^2-8>=-8
So minimum = - 8, no maximum

How to find the maximum or minimum value of quadratic function
How to find the maximum or minimum of quadratic function

The right half of the quadratic function is factorized and transformed into a complete square formula (with collocation method). Then we look at the positive and negative values of A. negative numbers have maximum values and positive numbers have minimum values. Then the last constant term is the maximum value

The minimum value of quadratic trinomial x2 + 5x + 7 is______ ．

X2 + 5x + 7 = x2 + 5x + 254 + 34 = (x + 52) 2 + 34 ≥ 34, then the minimum value of quadratic trinomial x2 + 5x + 7 is 34

RELATED INFORMATIONS

1. If x ^ 2 + 2 (M + 3) x + m ^ 2 + 3 = 0 has two real roots a and B, what is the minimum value of (A-1) ^ 2 + (B-1) ^ 2?
2. If the quadratic equation x ^ 2 + 2 (M + 3) x + m ^ 2 + 3 = 0 has two real roots a and B, what is the minimum value of (A-1) ^ 2 + (B-1) ^ 2?
3. The coefficient of quadratic term of quadratic function f (x) is a. and the solution set of inequality f (x) > 2x is (- 1.3). If f (x) = - 7a has two equal real roots, find the analytic solution of F (x)
4. It is known that the factorization result of the quadratic trinomial ax + bx-2 of X is (x + 1) (x-C), and the value of ABC is obtained
5. In the product of (^ 2-mx + 1) (X-2), if the coefficient of two terms of X is 0, then the value of M is zero
6. If the quadratic coefficient of X in the product of [x & sup2; - MX + 1] [X-2] is zero, then the value of M is [] Good play + 20
7. It is known that the sum of the first three terms of the arithmetic sequence {an} is - 3, and the product of the first three terms is 8
8. It is known that the sum of the first three terms of the arithmetic sequence {an} is - 3, and the product of the first three terms is 8 (1) The general term formula of {an} (2) A3 & # 178; = a2a1, find the sum of the first n terms of the sequence {| a}
9. Known sequence 1,5,9 The general formula of 101 is an; arithmetic sequence 3,5,9,15 The general term formula of 105 is BN to find the same term of {an} and {BN}
10. Given that the first three terms of the arithmetic sequence are A-1, a + 1 and a + 3, what is the general term formula of the sequence?
11. Write a quadratic equation of one variable with quadratic coefficient 1 and two equal real roots
12. Given that x2 + ax-12 = 0 can be decomposed into the product of the first-order factors of two integral coefficients, then the number of qualified integers a is______ ．
13. There are () integers n between 1 and 1990, which can make x 2 + x-3 n decompose into the product of two integral coefficients A. 1990B. 75C. 50D. 44
14. How many integers are there between 1 and 100 that can decompose x ^ 2 + x-n into the product of two factors (). Choose a: 0 B: 1 C: 2 D: 9 e: 10
15. When factoring a quadratic trinomial, student a misinterprets the coefficient of the first term and decomposes it into 2 (x-1) (X-9), while student B misinterprets the constant term and decomposes it into 2 (X-2) (x-4). Please judge the correct quadratic trinomial and decompose it correctly
16. When factoring a quadratic trinomial, student a misinterprets the coefficient of the first term and decomposes it into 2 (x-1) (X-9), while student B misinterprets the constant term and decomposes it into 2 (X-2) (x-4). Please judge the correct quadratic trinomial and decompose it correctly
17. (1) 36 (x + y) quadratic-49 (X-Y) quadratic (2) (x + y) quadratic / 4 - (X-Y) quadratic / 4
18. If the product of (x + m) and (x's square + MX + 3) does not contain the quadratic term of X, then the coefficient of the first term of X in the product is
19. If x is less than 2, what is the absolute value of 2x minus 5
20. It is known that the fourth binomial coefficient of the expansion of [(a-2b) to the nth power] is the largest, then the sum of the coefficients of the expansion is

Finding the maximum or minimum value of quadratic trinomial 2x ^ 2 + 8x