The coefficients a, B and C of quadratic function f (x) = ax ^ 2 + BX + C are not equal to each other, and they are all in - 4, - 3, - 2, - 1,0,1,2,3 (1) The parabola with the opening upward has___________ Article, (2) The parabola passing through the origin has_____________ Article

The coefficients a, B and C of quadratic function f (x) = ax ^ 2 + BX + C are not equal to each other, and they are all in - 4, - 3, - 2, - 1,0,1,2,3 (1) The parabola with the opening upward has___________ Article, (2) The parabola passing through the origin has_____________ Article

A:
（1）
If the opening is upward, it means that a > 0, take a value in 1,2,3
C3 takes 1 as a, the remaining 7 takes 1 as B, and the remaining 6 takes 1 as C
3 * 7 * 6 = 126
(2) When x = 0, f (0) = C = 0
A take 1 out of the remaining 7 values, and then take 1 out of the remaining 6 values as B:
7 * 6 = 42
The opening upward is a > 0, three
Through the origin (0, 0), that is, C = 0
a. B is chosen from the remaining seven numbers. There are 7 * 6 = 42 species
There are 126 openings upward
There are 42 crossing the origin
The coefficients a, B and C of quadratic function f (x) = ax ^ 2 + BX + C are not equal to each other, and they are all in - 4, - 3, - 2, - 1,0,1,2,3
(1) The parabola with the opening upward has_ 4x8x7=224__________ Article,
(2) The parabola passing through the origin has____ 42_________ strip
If the solution of the system of equations {5x + 2Y = K + 1,4x + 3Y = 3 satisfies X-Y 〉 2, then the value range of K is
{5x+2y=k+1,4x+3y=3
（5x+2y)-(4x+3y)=k+1-3
That is X-Y = K-2 > 2
k-2＞2
k＞4
Given the quadratic function f (x) = ax ^ 2 + BX + 1 (a > 0), f (x) = {f (x) (x > 0) - f (x) (x < 0)}, if f (- 1) = 0
For any real number x, f (x) ≥ 0 holds
(1) The expression of finding f (x)
(2) When x ∈ [- 2,2], G (x) = f (x) - KX is a monotone function, and the value range of K is obtained
（1）f(-1)=a-b+1=0,b=a+1,
For any real number x, f (x) ≥ 0 holds,
b^-4a=(a-1)^
Solve the equations 2x + 3Y = 5, - 5x-7y = 1
2x+3y=5
14x+21y=15
-5x-7y=1
-15x-21y=3
Two formula addition
14x-15x=15+3
-x=18
x=-18
3y=5-2x=5+2x18
3y=41
y=41/3
If you don't understand this question, you can ask,
2x+3y=5,…… (1)
-5x-7y=1…… II.
① X 5 + 2 x 2, y = 27,
Substituting y = 27 into 1 gives x = - 38,
∴X=-38，Y=27。
2x+3y=5
14x+21y=15
-5x-7y=1
-15x-21y=3
Two formula addition
14x-15x=15+3
-x=18
x=-18
3y=5-2x=5+2x18
3y=41
y=41/3
Hope to adopt
Given that a, B and C are in equal proportion sequence, then the number of intersections between the image and X axis of quadratic function f (x) = AX2 + BX + C is ()
A. 0b. 0 or 1C. 1D. 2
From a, B, C into an equal ratio sequence, we get B2 = AC, and AC > 0, let AX2 + BX + C = 0 (a ≠ 0), then △ = b2-4ac = ac-4ac = - 3aC < 0, so the number of intersections between the image of function f (x) = AX2 + BX + C and X axis is 0
Solving equations 2x + 3Y = 13,5x-7y = - 11
2x+3y=13(1)
5x-7y=-11(2)
(1) * 5 - (2) * 2 is 29y = 87, y = 3, substituting (1) x = 2
2x+3y=13 10x+15y=65
5x-7y = - 11, 10x-14y = - 22, y = 3, x = 2
2X + 3Y = 13, two sides multiply by 5 to get 10x + 15y = 65, 5x-7y = - 11, two sides multiply by 2 to get 10x-14y = - 22, left formula minus right formula to get 29y = 87, y = 3 and then substitute into the original equation to get x = 2
Given the quadratic function f (x) = ax ^ 2 + BX + C1), if a > b > C, and f (1) = 0, it is proved that the image of F (x) has two different intersections with x-axis
(2) It is proved that for x1, X2, there is x1-2
(1) Because f (1) = 0, we can get a + B + C = 0, we can get b = - (a + C) for quadratic function f (x) = ax & sup2; + BX + C, and the discriminant △ = B & sup2; - 4ac = (a + C) & sup2; - 4ac = (A-C) & sup2; > 0 (a > b > C, a ≠ C), so there are two different intersection points with X-axis (2) for f (x) = ax ^ 2 + BX + C, it is easy to know that its axis of symmetry is X
Find the equations, 5x-3y = 22 2x-7y = 90
5x-3y=22 （1）
2x-7y = 90 x = 3.5y + 45 substituting (1): 5 (3.5y + 45) - 3Y = 22 14.5y = 22-225 y = - 203 / 14.5 = - 14
x = －4
y = -14
In the function f (x) = AX2 + BX + C, if ABC is an equal ratio sequence and f (0) = 4, then f (x) has a maximum or a minimum? What is it?
Because ABC is an equal ratio sequence, B & # 178; = AC can be known as C = 4 by F (0) = 4. Therefore, B & # 178; = 4A, that is, a = B & # 178; / 4; so f (x) = ax & # 178; + BX + C = B & # 178; X & # 178; / 4 + BX + 4 = 1 / 4 (B & # 178; X & # 178; + 4bx) + 4 = 1 / 4 (BX + 2) &# 178
To solve the equations: 15x + 13y = 250.5x − 0.3y = 0.2
The results show that: 3x + 5Y = 6, ① 5x − 3Y = 2, ②, ① × 3 + ② × 5: 34x = 28, x = 1417, ① × 5 - ② × 3: 34y = 22, y = 1117, that is, the solution of the equations is x = 1417y = 1117