The parabola ax & # 178; + BX + C passes through points (0, - 1) and points (3,2). A < 0, the vertex is on the straight line y = 3x – 3. Find the analytic expression of the function

The parabola ax & # 178; + BX + C passes through points (0, - 1) and points (3,2). A < 0, the vertex is on the straight line y = 3x – 3. Find the analytic expression of the function

If the vertex is (m, 3m-3), then y = a (x-m) ^ 2 + 3m-3, so - 1 = a (0-m) ^ 2 + 3m-33 = a (2-m) ^ 2 + 3m-3 minus 4 = a (4-4m) a = 1 / (1-m) so - 1 = m ^ 2 / (1-m) + 3m-3, so M-1 = m ^ 2-3m ^ 2 + 6m-32m ^ 2-5M + 2 = 0 (2m-1) (m-2) = 0a1, so m = 2, so y = - x ^ 2 + 4x-1

Whether to judge the congruence of two triangles by "the diagonal correspondence of the two sides of the triangle and other sides is equal"
If you can explain it, you can't give counter examples

Yes
Isn't this a theorem of congruence of triangles
The angles between the two sides are equal, and the two triangles are congruent

If the monotone decreasing interval of function f (x) = 4x ^ 3-ax 3 is (- 1 / 2,1 / 2), then the value of real number a is________ .
ax+3
Sorry, I didn't

a=3
Using derivative calculation:
（x）=12x^2-a
The monotone decreasing interval of function is (- 1 / 2,1 / 2)
Note that - 1 / 2 and 1 / 2 are roots of 12x ^ 2-A = 0
So 12 * (1 / 4) - a = 0, so a = 3

Who can help me to solve 20 factoring problems in Volume 1 of Grade 8

A quadratic function y = - 3 / 3 change sign 3x square + - 2 / 3 change sign 3 + change sign 3
Let a (- 3,0) C (0, change number 3) B (1,0), m, n move along Ba, BC with a unit length. Suppose the movement time is t, the triangle BMN is folded along Mn, B falls on point P on the side of AC, and the coordinates of T and P are obtained. There is a point Q on the symmetry axis of this quadratic function, so that the triangle BNQ is similar to the triangular ABC, and the coordinates of point q are obtained
With the function relation and ABC coordinate, can't you draw the graph yourself? Besides, I didn't get the title

BN = NP = PM = MB = t
And in △ BMN, tanb = = √ 3, so

Is the solution of 3x + 5x = x + 7 1 or x = 1
Or both?

It should be x = 1, and the specific value of X is the solution of the original equation
It's a matter of format~
Cannot write 1

If there are two intersections between the parabola y = x2 + (2m-1) x + m2 and the X axis, what is the value range of M?

There are two intersections with X axis, that is, x ^ 2 + (2m-1) x + m ^ 2 = 0 has two unequal real roots
Δ=(2m-1)^2-4m^2=1-4m>0
m

The application of the problem of chasing and meeting

1. A bridge is 700 meters long. Two people go for a walk on the bridge at the same time. They walk opposite each other from the north and south ends of the bridge. Uncle Wang walks 20 meters every minute, Uncle Li walks 15 meters every minute. After the first meeting, they both stay for one minute, and then continue to walk forward. When they reach the two ends of the bridge, they return immediately. After the second meeting, they meet again

Given a point Q (2,0) and a circle C: x2 + y2 = 1 in rectangular coordinate system, the tangent length from the moving point m to the circle C is equal to the sum of the radius of the circle C and MQ, the trajectory equation of the moving point m is obtained

The coordinate of M is (x, y) the tangent length from the condition of (x, y) the tangent length from the condition of (x, y) the coordinate of M is (x, y) the tangent length from the condition of (x, y) the condition of the tangent length of MP = (x, y) the condition of MP = (x, y) the condition of the tangent length of MP (x, y) is the condition of the tangent length of MP = (MC & \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\35;178; + Y & #178; 2x-3 = √ (X-2

The equation (3x + 2) ∧ 2 + (X-5) - (3x + 2) (X-5) = 49 is reduced to the general form

3x∧2+13x-20=0