(of quadratic function) 1. State the opening direction, axis of symmetry and vertex coordinates of the following parabola ⑴,y=1/3(x-5/3)^2+2/3 ⑵,y=-0.7(x+1.2)^2-2.1 ⑶,y=15(x+10)^2+20 ⑷,y=-1/4(x-1/2)^2-3/4 2. The following functions are reduced to the form of y = a (X-H) ^ 2 by the collocation method (1)y=x^2+4+5 (2)y=2x^2+4x 3. The vertex coordinates of parabola y = - 12x2 + 2x + 4 are_______ The axis of symmetry is_______ ； 4. The maximum value of quadratic function y = AX2 + 4x + A is 3, and the value of a is obtained 5. If the coordinates of any three points on the image of a quadratic function are known, the general formula (a ≠ 0) is used to find the analytic formula 6. Given the parabola y = 4 (x-3) ^ 2-16, write its opening direction, axis of symmetry and vertex coordinates 7. Determine the opening direction of parabola according to vertex formula__ The axis of symmetry is____ The vertex coordinates are____ .

(of quadratic function) 1. State the opening direction, axis of symmetry and vertex coordinates of the following parabola ⑴,y=1/3(x-5/3)^2+2/3 ⑵,y=-0.7(x+1.2)^2-2.1 ⑶,y=15(x+10)^2+20 ⑷,y=-1/4(x-1/2)^2-3/4 2. The following functions are reduced to the form of y = a (X-H) ^ 2 by the collocation method (1)y=x^2+4+5 (2)y=2x^2+4x 3. The vertex coordinates of parabola y = - 12x2 + 2x + 4 are_______ The axis of symmetry is_______ ； 4. The maximum value of quadratic function y = AX2 + 4x + A is 3, and the value of a is obtained 5. If the coordinates of any three points on the image of a quadratic function are known, the general formula (a ≠ 0) is used to find the analytic formula 6. Given the parabola y = 4 (x-3) ^ 2-16, write its opening direction, axis of symmetry and vertex coordinates 7. Determine the opening direction of parabola according to vertex formula__ The axis of symmetry is____ The vertex coordinates are____ .

1. (1) (2) (3) (4) 6. Opening direction: upward downward upward upward symmetry axis: straight line x = 5 / 3 straight line x = - 1.2 straight line x = - 10 straight line x = 1 / 2 straight line x = 3 vertex coordinates: (5 / 3,2 / 3) (- 1.2,2.1) (- 10,20) (1 / 2, - 3 / 4) (3, - 16) 2. Y = x ^ 2 + 9, y = 2 (x + 1) ^ 2-2 3

If | x ^ 2-4x + 3 | = MX has four unequal real roots, then the value range of real number m is?
Given that y = f (x) is an even function and a decreasing function from 0 to positive infinity, then the monotone increasing interval of F (1-x ^ 2) is?

1 m greater than 0 less than 1 (drawing) quadratic function has absolute value to turn up_______________________ The solution of this equation is the intersection of two images, that is, four intersections. You put two pictures together to find the range of four intersections

According to the following conditions, the analytic expression of quadratic function is obtained
① The parabola y = ax ^ 2 + BX + C passes through three points (0,1), (1,3), (- 1,1). ② the vertex P (- 1, - 8) of the parabola passes through point a (0, - 6). ③ the image of the quadratic function y = ax ^ 2 + BX + C passes through two points (3,0), (2, - 3) and takes x = 1 as the axis of symmetry

Solution 1: substitute x = 0, y = 1; X = 1, y = 3; X = - 1, y = 1 into y = ax & # 178; + BX + C to get the equations of a, B, C: C = 1A + B + C = 3a-b + C = 1 to solve the equations of a = 1, B = 1, C = 1, the analytic formula of parabola is y = x & # 178; + X + 1 solution 2: let the analytic formula of parabola be vertex formula y = a (x + 1) &# 178; - 8, let x = 0

According to the following conditions, the analytic expressions of quadratic functions are obtained respectively
(1) The vertex coordinates of known image are (- 1. - 8) tangent point (0. - 6)
(2) It is known that the image passes through the point (3.0) (2. - 3) and takes the line x = 0 as the symmetry axis

1. Let y = a (x + 1) ~ - 8
=ax~+2ax+a-8
y'=2ax+2a
Bring in (0, - 6) to get a = - 3
y=-3x~-6x-11
2. Let y = ax ~ + B
Substituting (3,0) (2, - 3)
A = 3
b=-9