The axis of symmetry of the parabola y = (M2-2) x2 + 2mx + 1 with downward opening passes through the point (- 1,3), and the value of M is obtained

The axis of symmetry of the parabola y = (M2-2) x2 + 2mx + 1 with downward opening passes through the point (- 1,3), and the value of M is obtained

∵ the symmetric axis of the parabola y = (M2-2) x2 + 2mx + 1 with downward opening passes through the point (- 1,3), ∵ - 2M2 (M2-2) = - 1, M2-2 < 0, and the solution is: M1 = - 1, M2 = 2 (not suitable for the problem), and∵ M = - 1
Solving the quadratic equation 2x-4x = 5
4x-3y=5 ①
2x-y=-5 ②
② X 2
4x-2y=-10③
③ - 2
-y=-15
y=15
Substituting y = 15 into (2) d yields
2x-15=-5
2x=10
X=5
The solution of the equations is x = 5
y=15
If you have any questions, please ask
Given that point a (3, - 1) is on the parabola y = x ^ 2-2mx + m, if point B and point a are symmetrical about the parabola axis. Q: is there a straight line intersecting with the parabola at only one point B? If so, find out the analytical formula of the straight line that meets the condition; if not, explain the reason
Let y = KX + B (K ≠ 0) pass through B (1, - 1), and then B = - 1-k
Binary linear equations: 4x-3y = 7,2x-3y = - 1,
X = 4, y = 3, do you want to solve the problem or not? Take formula 2 to get x = 3y-1 / 2. Take Formula 1 to get y = 3 to get x = 4
x=4.y=3
x=4 y=3
X=4
Y=3
X=4，y=3
x=4y=3
X=4，Y=3
Formula 4x-3y = 7 -- (1)
Formula 2x-3y = - 1 -- (2)
(2) The formula changes to 3y-2x = 1 -- (3)
(1) + (3) get 2x = 8
The solution is x = 4
Substituting into the original equation, y = 3
x=4，y=3
If {x = - 1, y = 2} is the solution of the system of equations {ax-4y = 3,3x + by = 5}, then a = (- 11), B = (4) 2. The system of quadratic equations with {x = 3My = - 5} as the solution is ({x + 3My = 10, x-3my = 0}) (just write one) 3. It is known that {x = - 1, y = 2} and {x = 2, y = C} are equations 2x + y = m, then C = - 4 1, {x + y = 128, X-Y = 4} x = 4 + y, x + y = 128, y = 62... Expand
If {x = - 1, x = 1, x = 1, y = 2} is the solution of the equation system {{ax-4y = 3,3x + 3x + by = 5}, then a = (-11), B = (4) 2, 2, the binary linear equation system for the solution of {x = 3My = -1, y = 3, y = 10, x-3my = 10, x-3my = 10, x-3my = 0 (only write one to write one) (just write one to write one can write only one only write one) only write one can write one can write one can write one (3) 3, we know that {{x = {x = -1, y = 1, y = 1, y = 1, y = 1, y = 1, y = 1, y = 1, y = 1, y = 2, y = 2, y = 2, y = 2, y = 2, y = 2, y = 2, y = 2, y = 2 and {y = 2x, 4x + 3Y = 65} 4x + 3Y = 65, Y = 2x 4x + 3 * 2x = 65, x = 6.5, y = 13.3, {2x-5y = 7,2x + 3Y = - 1} are subtracted to get - 8y = 8, y = - 1, x = 14, {3x-2y = 9, x + 2Y = 3} and are added to get 4x = 12, x = 3, y = 0. Solve the equation {4x = 3Y + 2 ①, 4x-2y = 11, ②}. Take "4x" as a whole, and bring ① into ② to get (3Y + 2-2y = 11 (i.e., y + 2 = 11))
X=4
Y=3
X=4
Y=3
Process {x = (3y-1) / 2
4*(3y-1)/2-3y=7 }
X=4 y=3
Given that the two intersections of parabola y = x ^ 2 + 2mx + M-7 and X axis are on both sides of (1,0), what is the value range of M?
RT
X1 = - m-root (m ^ 2-m + 7) 1, square root
From the two intersection points of parabola f (x) = x ^ 2 + 2mx + M-7 and X axis on both sides of point (1,0), we can get that,
f(1)
Y = 3x-1 4x-3y = 5 using substitution method to solve binary linear equations
If y = 3x-1 is replaced by 4x-3y = 5, then y = 3x-1 is replaced by 4x-3y = 5
4x-3(3x-1)=5
4x-9x+3=5
-5x=2
Substituting x = - 2 / 5 into y = 3x-1, we get: x = - 2 / 5, y = 3x-1
y=-6/5-1=-11/5
So: x = - 2 / 5, y = - 11 / 5
Substituting Formula 1 into formula 2 leads to the following result:
4X-3（3X-1）=5
-5X=5-3
X = - 2 / 5, substituting 1 to get y = - 6 / 5-1 = - 11 / 5.
y=3x-1 （1）
4x-3y=5 （2）
Substituting (1) into (2)
4x-3*(3x-1)=5
-5X=5-3
X=-2/5
Substituting (1)
y=-11/5
y=3x-1
4x-3y=5
===> 4x-3(3x-1)=5
===> 4x-9x+3=5
===> 5x=-2
===> x=-2/5
Then, y = 3x-1 = (- 6 / 5) - 1 = - 11 / 5
To sum up: x = - 2 / 5, y = - 11 / 5
It is known that the two intersections of parabola = x2 + 2mx + m - 7 and X-axis are on both sides of point (1,0)
Given that the two intersections of parabola = x2 + 2mx + m - 7 and X axis are on both sides of point (1,0), then the root of equation x2 + (M + 1) x + M2 + 5 = 0 is ()
(A) There are two positive roots (b), two negative roots (c), one positive root and one negative root (d). There is no real root
Please explain clearly,
The two of F (x) = x2 + 2mx + m - 7 are beside (1,0)
Imagine a function diagram
Is it f (1)
(D) No real root
Solution: ∵ the two intersections of function y = x ^ 2 + 2mx + M-7 and X axis are on both sides of (1,0)
The two real roots of equation 0 = x ^ 2 + 2mx + M-7 are outside (1,0)
∴△=b^2-4ac=4m^2-4(m-7)=4m^2-4m+28＞0
f(1)=1+2m+m-7=3m-6＜0
∴m＜2
f(0)=m-7＜0
∴m＜7
∵ m ＜ 2, m ＜ 7
(D) No real root
Solution: ∵ the two intersections of function y = x ^ 2 + 2mx + M-7 and X axis are on both sides of (1,0)
The two real roots of equation 0 = x ^ 2 + 2mx + M-7 are outside (1,0)
∴△=b^2-4ac=4m^2-4(m-7)=4m^2-4m+28＞0
f(1)=1+2m+m-7=3m-6＜0
∴m＜2
f(0)=m-7＜0
∴m＜7
∵m＜2,m＜7
∴m＜2
The discriminant of x ^ 2 + (M + 1) x + m ^ 2 + 5 = 0
△=(m+1)^2-4(m^2+5)=-3m^2+2m-19
Now let's look at this equation about M, the discriminant of this equation
△=2^2-(-3*(-19))
{x+3y=5 ,3x-6y=6
x+3y=5①
3x-6y=6②
From (1): x = 5-3y is substituted into (2)
3（5-3y)-6y=6
15-9y-6y=6
-15y=-9
y=3/5
∴x=5-3×3/5=16/5
That is: the solution of the equations is: x = 16 / 5; y = 3 / 5
It is known that the two intersections of parabola y = x ^ 2 + 2mx + M-7 and X axis are on both sides of point (1,0),
Given that the two intersection points of parabola = x ^ 2 + 2mx + M-7 and X axis are on both sides of point (1.0), then the case about the root of X equation 1 / 4x ^ 2 + (M + 1) x + m ^ 2 + 5 = 0 is
From the two intersection points of parabola f (x) = x ^ 2 + 2mx + M-7 and X-axis on both sides of point (1,0), we get that f (1)
If the solution of the binary linear simultaneous equation 2x − 3Y6 = 415x + 15y − 53 = 0 is x = a, y = B, then A-B = ()
A. 53B. 95C. 293D. −1393
Firstly, by simplifying the equations, we get 2x − 3Y = 24, ① 3x + 3Y − 1 = 0, ② ① + ②, we get 5x = 25, that is, x = 5. Y = - 143. ∵ x = a, y = B, ∵ A-B = X-Y = 5 - (- 143) = 293