The definition of quadratic function

The definition of quadratic function

Generally, a function of the form y = ax ^ 2 + BX + C (a ≠ 0) is called a quadratic function. The independent variable (usually x) and the dependent variable (usually y). The right side is an integral, and the highest degree of the independent variable is 2

I know how to judge the sign of ABC, but I don't know what's the use of the number on the point. For example, when image a passes through the symmetry axis of point a (- 3,0), x = - 1 1: B bisection ＞ 4ac 2:2a + B = 0 3: A-B + C = 0 4:5a ＜ B, how to judge how to use this number?

Let f (x) = the square of a x + B x + C, from the axis of symmetry x = - 1, we get - B / 2A = - 1, that is, B = 2A, from the passing point (- 3,0), we get 9a-3b + C = 0, and 3a + C = 0, from the passing point (- 3,0) axis of symmetry x = - 1, we can get another zero point (1,0)

Given the ABC three-point coordinates on the image of quadratic function, find the analytic expression of this function

y=ax²+bx+c
Substitute the coordinates of the three points in
The system of linear equations with three variables is obtained
We can solve a, B and C

According to the condition, the analytic expression of quadratic function is obtained. It is known that the symmetric axis of parabola passing through point a (- 1,0) B (0,6) is a straight line x = 1

Let the equation be y = a (x-1) &# 178; + B
Bring the coordinates of points a and B into
0=4a+b
6=a+b
A = - 2
b=8
Then y = - 2 (x-1) &# 178; + 8

1. It is known that the symmetry axis of the parabola is x = 1, and through (4,5) (- 1,0), find its analytical formula. 2. It is known that the image of quadratic function passes through the point P (2,0) Q (6)

If the axis of symmetry is x = 1, then y = ax ^ 2 + BX + C can be solved through point (1,0) (4,5) (- 1,0) to get y = 1 / 3x ^ 2-1 / 3
. what's the next problem?

If we know the parabola a (1,0), B (0, - 3) and the axis of symmetry is x = 2, how to find the analytical formula of the parabola!

Since the axis of symmetry x = 2, let y = a (x - 2) & # - 178; + H substitute (1, 0) and (0, - 3) into: a + H = 04A + H = - 3, the solution is: a = - 1H = 1, so y = - (x - 2) & # - 178; + 1, that is, y = - X & # - 178; + 4x - 3

The analytical formula of parabola with Y-axis passing through point a (1,3) and point B (- 2, - 6) is______ ．

Let the parabolic equation be: y = AX2 + BX + C (a ≠ 0); ∵ the symmetry axis of the parabola is Y axis, ∵ x = - B2A = 0, ∵ B = 0; and ∵ the parabola passes through point a (1,3), point B (- 2, - 6), ∵ 3 = a + B + C, ② - 6 = 4a-2b + C. ③ from the solution of ①, ②, ③, a = - 3; b = 0, C = 6, ∵ the analytical solution of the parabolic equation is as follows

It is known that the symmetry axis of quadratic function is x = 2, and the image passes through (1,4), (5,0) two points, and the analytical expression of parabola is obtained

Let the analytic formula y = ax * x + BX + C x = 2 = - B / 2a, B = - 4A, and substitute (1,4), (5,0) into the analytic formula to find a, B, C

If the image of the first-order function passing through point (2,1) is parallel to the straight line y = - 2x + 3, then the expression of this function is? (explain the reason)

Analysis
Because parallel K is equal
therefore
y=-2x+c
Substituting (2,1) into
-2*2+c=1
c=5
So the linear equation y = - 2x + 5

If the image of a function of degree passes through a point (1, - 1) and is parallel to the line y = 5-2x, then the expression of the function of degree is____ ?

According to the meaning of the title, it can be set
The function is y = - 2x + B
Another point (1, - 1)
Namely
-1=-2+b
b=1
therefore
The expression is y = - 2x + 1