How to roll out the two point formula of a quadratic function

Find the quadratic function.

The analytic formula is one of the key and difficult points in this chapter on functions.

Find the analytic formula of the function.

The general steps are:

Set up the general analytic expression of the desired function.

Treat the coefficients in the analytic equation as unknowns.

List equations or systems of equations.

Find the solution of an equation or system of equations.

Then substitute the function analytic formula to get the desired analytic formula.

where it can be based on some of the relevant properties of the function or some of the conditions it satisfies.

The analytic formula of the function is the key to finding the analytic formula of the quadratic function.

There are generally three forms of analytic expressions for quadratic functions. General. yax2bx+c(a≠

abc is a constant. Vertex style.

ya(x-h)

k(a≠ahk is constant. Two-point. ya(x

x1)xx2a≠

ax1,x2

is constant. Reasonable set two....

Resources. Hope the above answers can help you.

The general formula of a quadratic function is y=ax2+bx+c(a≠0), where x is the independent variable.

For zero-point (two-point, two-point), you can sort out y=a(x-x1)(x-x2) that you gave

Here, a is the quadratic coefficient, x is an independent variable like x in the general equation, and x1 and x2 are the abscissa of the intersection of the function image and the x-axis. Therefore, this analytic formula only applies to the formula of 0.

Quadratic functionsThe two-point formula (or intersection formula) is: y=a(x-m)(x-n), where m,n is the abscissa of the quadratic function and the two intersections of the x-axis.

Quadratic function analytic form:

1.General formula: y ax2+bx+c (a, b, c are constants, this is like a≠0), then y is called a quadratic function of x. Vertex coordinates.

b/2a,(4ac-b2)/4a)

2.Vertex formula: y a(x-h)2+k or y=a(x+m)2+k (a, h, k are constants, a≠0).

3.Intersection (and x-axis): y=a(x-x1)(x-x2) (also known as two-point formula, two-branch Hegen formula.)

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The maximum value of the quadratic function is asked the Mori fiber problem

The general formula of the quadratic function is y ax2+bx+c, when a is greater than 0, the opening is upward, and the function has a minimum value; When a is less than 0 and the opening is downward, the function has a maximum value.

The vertex coordinates are (b -2a, (4ac-b2) 4a), which is to substitute a, b, and c respectively to find the coordinates of the vertices. (4ac-b2) 4a is the maximum.

Let the quadratic function be.

Intersect with the x-axis a(x1,0)b(x2,0), then the quadratic function can be expressed as y=a(x-x1)(x-x2).

For example, the quadratic function image intersects with the x-axis at two points, (1,0)(4,0), and passes through the points (2,4) to find its analytic formula.

Solution: Let the analytic formula be y=a(x-1)(x-4), and substitute the coordinates of (2,4) points into the :

4=a (2-1) (2-4)

Solution: a=-2

So the analytic formula is: y=-2(x-1)(x-4) or y=-2x2-10x-8;

In general, the two-point method is used to find the analytic formula, let y=a(x-x1)(x-x2), where x1,x2 is the abscissa of the intersection point of the image and the x-axis, and the abscissa of the intersection point in this case is 1 and 4.

y=a（x-x1）（x-x2）。where x1 and x2 are the two roots of the equation y=ax2+bx+c(a≠0).

The two-point formula is also called the two-root formula, the two-point formula: y a(x-x1)(x-x2), where x1, x2 is the abscissa of the intersection of the parabolic shed back stool and the x-axis, that is, the two roots of the unary quadratic equation ax2+bx+c 0, a≠0.

Knowing the two intersection points of the parabola and the x-axis (x1,0),(x2,0), and knowing that the parabola passes through a certain point (chain travel m,n), let the equation of the parabola be y=a(x-x1)(x-x2), and then substitute the points (m,n) to obtain the quadratic coefficient.

Let the quadratic function intersect with the x-axis at a(x1,0)b(x2,0), then the quadratic function can be expressed as y=a(x-x1)(x-x2).

It is known that the parabola intersects (-1,0) and (3,0) with the x-axis, and then (0,3), and the parabola is found analytically.

Let the parabola analyze the Dan boring formula: y=a(x+1)(x-3), and then (0,3), and bury the tomb:

3=a(0+1)(0-3),a=-1,y=-(x 2-2x-3), i.e., mold bend y=-x 2+2x+3

1. You can directly derive two of the equations.

y=a(x-x1)(x-x2)。where x1 and x2 are the two roots of the equation y=ax2+bx+c(a≠0).

The two-point Tong Hall mold is also called the two-root type.

Two-point formula: y a(x-x1)(x-x2), where x1,x2 is the abscissa of the intersection of the parabola and the x-axis, i.e., the two roots of the unary quadratic equation ax2+bx+c 0, a≠0.

2. Obtain the intersection point with the x-axis.

Know the two intersections of the lodging deficit with the x-axis (x1,0),(x2,0).

y=a（x-x1）（x-x2）。where x1 and x2 are the two roots of the equation y=ax2+bx+c(a≠0).

The two-point formula is also called the two-point formula, the two-point formula: y a(x-x1)(x-x2), where x1, x2 is the abscissa answer of the intersection point of the parabolic line and the x-axis, that is, the two roots of the unary quadratic equation ax2+bx+c 0, a≠0.

Knowing the two intersection points of the parabola and the x-axis (x1,0),(x2,0), and knowing that the parabola passes through a certain point (m,n), let the equation of the parabola be y=a(x-x1)(x-x2), and then substitute the points (m,n) to obtain the quadratic coefficient a.

In general, there is a relationship between the independent variable x and the dependent variable y:

1) General formula: y ax2+bx+c (a, b, c are constants, a≠0), then y is called a quadratic function of x. Vertex coordinates (-b 2a, (4ac-b 2) 4a).

2) Vertex formula: y a(x-h)2+k or y=a(x+m) 2+k(a,h,k is constant, a≠0)

3) Intersection (with x-axis): y=a(x-x1)(x-x2).

4) Two roots: y a(x-x1) (x-x2), where x1, x2 is the abscissa of the intersection of the parabola and the x-axis, that is, the two roots of the unary quadratic equation ax2+bx+c 0, a≠0

Description: (1) Any quadratic function can be converted into vertex formula y a(x-h)2+k through the formula, the vertex coordinates of the parabola are (h,k), when h 0, the vertex of the parabola y ax2+k is on the y axis; When k 0, the vertex of the parabola a(x-h)2 is on the x-axis; When H0 and K 0, the vertex of the parabola y ax2 is at the origin.

2) When the parabola y ax2+bx+c has an intersection point with the x-axis, that is, when the corresponding quadratic equation ax2+bx+c 0 has real roots x1 and x2, according to the decomposition formula of the quadratic trinomial ax2+bx+c a(x-x1)(x-x2), the quadratic function y ax2+bx+c can be converted into two arrows y a(x-x1)(x-x2)

Let the quadratic function intersect with the x-axis at a(x1,0)b(x2,0), then the quadratic function can be expressed as y=a(x-x1)(x-x2).