(primary, quadratic, inverse function) I'm so anxious. I need it for review!

Y = KX + B (once)
Y = ax ^ 2 + BX + C (twice)
Y = A / x + C (inverse proportion)

What is the vertex formula of the fishhook function

Check function y = x + A / X (a > 0)
The vertices of are (√ a, 2 √ a) and (- √ a, - 2 √ a)

What is the formula for generalizing the vertex formula of quadratic function

Y = ax ^ 2 + BX + C into vertex formula: y = a (x + B / 2a) ^ 2 + (4ac-b ^ 2) / 4A

Given the vertex coordinates of the parabola, find the function expression RT, given the vertex coordinates (3, - 2), find the expression. I remember a formula, right? But because I haven't touched Math for years, ① : - B / 2A = 3 ②: 4ac-b ^ / 4A = - 2 can't calculate the values of a, B and C. It seems that there is a formula that knows the vertex coordinates and can directly deduce the expression (in school, the teacher seems to call it vertex type)

y = k(x -3)^2 - 2

Given the vertex coordinates (2,3) of the parabola and passing through points (3,1), find its function expression

solution
∵ known vertex coordinates (2,3)
Set the parabola as:
Y = a (X-2) square + 3
∵ process (3,1)
‡ a (3-2) square + 3 = 1
∴a+3=1
∴a=-2
‡ y = - 2 (X-2) square + 3

Given that the vertex of the parabola is (- 1,1), and the image passes through points (1, - 3), find the expression of this function

Let the equation be y = a (x-m) ²+ n
Bring in vertex coordinates (- 1,1)
Get: y = a (x + 1) ²- one
Then bring (2,1) into
Get 1 = a (2-1) ²- one
a=2
The analytical formula is y = a (x-1) ²- one
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(primary, quadratic, inverse function) I'm so anxious. I need it for review!