The parabola passes through the point (0.3); (1.0); (3.0)

The parabola passes through the point (0.3); (1.0); (3.0)

The parabolic equation can be set as follows:
y=a(x-1)(x-3), a≠0
3 = 3A
∴a=1.
The parabolic equation:
y=(x-1)(x-3)
=x²-4x+3

The relation between x-axis and parabola of quadratic function?

If the parabolic equation is y2 = 2px, then the parabola is symmetric about X axis;
If the parabolic equation is x2 = 2PY, then the parabola is tangent to the X axis at the origin;
If the parabolic equation is y = ax ^ 2 + BX + C, let △ = B ^ 2-4ac, then
When △ 0, the parabola intersects the X axis at two different points

Quadratic function (parabola)
The parabola y = AX2 + BX + C and a focus a of x-axis lie between (- 2,0) and (- 1,0) (including the two points). The vertex C is a moving point on the rectangular defg (including the boundary and interior), where d (1,3) e (1,2) f (3,2) g (3,3). What is the value range of a?

First of all, a

The translation of the parabola of quadratic function
There are two ways to change [1] into the vertex formula y = a (X-H) &# 178; + K left plus right minus, up plus down minus, which is well known. [2] for example, y = 2x & # 178; - 3x-1 moves 4 units to the left and 2 units to the up, that is, y = 2 (x + 4) &# 178; - 3 (x + 4) - 1-2. How can we get method 2? (that's the principle of method 2)

In fact, it's very easy to understand that the principle of left plus right minus, up plus down minus of vertex type and the second method is obtained through the invariance of abscissa or ordinate. ①: when moving left to right, the ordinate of each point is invariable, so the abscissa of each point should be added and subtracted to realize visual translation. To change x, we need to use y to express x, that is, how much x = y, To put it bluntly, we still need to reduce to the left, so it is x = how much Y - 2 (two units to the left). Move - 2 to x + 2 = how much y, and then replace x + 2 with the original x to get the result after translation. So we call it left addition (right subtraction is the same) for the sake of remembering, and understand it as not to be confused, When moving up and down, the abscissa of each point is unchanged, so just change the ordinate, that is, change y. there is a form of y = how much x, then you can directly add or subtract. Upward must add, downward must subtract. Because of different representation methods, it is just opposite to left plus right minus