Some concepts of quadratic function Y = a (X-H) + K, if the vertex coordinates are (5,8) or (- 5, - 8) Can it be reduced to y = a (X-5) square + 8 or y = a (x + 5) square-8? What do h and K mean? Also, if you want to translate the parabola y = ax right or left n units respectively In y = a (x? H), which side is the addition and which side is the subtraction? Is the sign of H always the same?

Some concepts of quadratic function Y = a (X-H) + K, if the vertex coordinates are (5,8) or (- 5, - 8) Can it be reduced to y = a (X-5) square + 8 or y = a (x + 5) square-8? What do h and K mean? Also, if you want to translate the parabola y = ax right or left n units respectively In y = a (x? H), which side is the addition and which side is the subtraction? Is the sign of H always the same?

X = h is the axis of symmetry and K is the ordinate of the vertex
Translate n units to the right or left in y = ax direction
Add to the left and subtract to the right, for example, translate n units to the right in the direction of y = ax to get the power of y = a (x-n)

An approach to the analytic expression of quadratic function

According to the conditions given to you by the title, it can be divided into three types
1： If the title gives the coordinates of three points on the parabola: a (x1, Y1), B (X2, Y2), C (X3, Y3)
Let the analytic formula of quadratic function be y = ax ^ 2 + BX + C
By substituting the coordinates of three points, a set of cubic equations with three variables is obtained
ax1^2+bx1+c=y1
ax2^2+bx2+c=y2
ax3^2+bx3+c=y3
Solve this group of cubic equations, and get a, B, C respectively, and then substitute y = ax ^ 2 + BX + C,
We can get the analytic expression of the original quadratic function
2： If the topic gives the vertex coordinates P: (h, K) on the parabola and the coordinates of another point on the parabola: a (x1, Y1)
Let the analytic expression of quadratic function be y = a (X-H) + K
Substituting the coordinates of another point, we get a one variable linear equation
a(x1-h)+k=Y1
We solve this equation of one variable and get a, and then substitute y = a (X-H) + K,
The analytic expression of the original quadratic equation can be obtained
3： If the topic gives the intersection of the parabola and the X axis: a (x1,0), B (x2,0) and the coordinates of another point:
C（x3,y3）
Let the analytic expression of quadratic function be y = a (x-x1) (x-x2)
Substituting the coordinates of another point, we get a one variable linear equation
a(x3-x1)(x3-x2)=y3
Solve the equation of one variable and get a, and then substitute y = a (x-x1) (x-x2),
The analytic expression of the original quadratic equation can be obtained

Analytic expression of quadratic function (all)

General formula: y = ax ^ 2 + BX + C (a is not equal to 0) vertex [- B / 2a, (b ^ 2-4ac) / 2A]
Vertex formula: y = a (X-H) ^ 2 + K (a is not equal to 0), vertex (h, K)
The intersection formula: y = a (x-x1) (x-x2) (a is not equal to 0), where X1 and X2 are the abscissa of the intersection X axis