What is the inverse function of the square of X + X + 2 = y? It's best to have a process

What is the inverse function of the square of X + X + 2 = y? It's best to have a process

x^2+x+2=y
x^2+x+1/4=y-3/4
(x+1/2)^2=y-3/4
X + 1 / 2 = radical (Y-3 / 4)
X = radical (Y-3 / 4) - 1 / 2
Then just change the XY letter

Inverse function y = x ^ 3 + 4 (x ∈ R)
How to solve it

Y = root of degree 3 (x-4)

What is the maximum value of quadratic function y = - x square + 4x-6

Y = - x squared + 4x-6
=-(x²-4x+4)-2
=-(x-2)²-2
The maximum value is y = - 2 when x = 2

If the maximum value of quadratic function y = - x2-4x + 2m2-m + L is equal to 5, then M = ()
Seek the process!

If the maximum value of quadratic function y = - x2-4x + 2m2-m + L is equal to 5, then M = (0 or 1 / 2)
y=-x²-4x+2m²-m+1
=-(x+2)²+2(m-1/4)²+39/8
2(m-1/4)²=5-39/8=1/8
M = 0 or M = 1 / 2

If the maximum value of quadratic function y = - x2-4x + 2m2-m + 1 is equal to 5, what is the value of M

The formula is y = - (x + 2) ^ 2 + (2m ^ 2-m + 5), because the parabolic opening is downward, and the vertex coordinate is (- 2,2m ^ 2-m + 5), so when x = - 2, the maximum value of the function is (2m ^ 2-m + 5), and it is known that the equation 2m ^ 2-m + 5 = 5, that is, 2m ^ 2-m = 0, m (2m-1) = 0, so m = 0 or M = 1 / 2, that is, the value of M is 0 or 1 / 2

When x takes what value, find the maximum and minimum of the following functions
1.y=x+(2/x)
2.y=(3x^2)+(1/(3x^2))
Actually, I added the brackets myself,
I can think of it just by looking at it, eh~

1: It's disgusting to play. You can't write sub input method. First, you turn the square of the root of X, 2 / x, into the square of the root of X, and then - 2 root sign 2, add 2 root sign 2 to form a complete square (the root of the root of X - 2 / x) minus 2 root sign 2, but root sign x = 2 / X of the root of X, and the minimum value is 2 root signs

1. The analytic formula of parabola with vertices (- 2, - 5) and passing through points (1, - 14) is________
2. The analytical formula of the parabola passing through a (1,3) B (- 2, - 6) is________
3. The length of the line cut by the parabola y = - 2x & sup2; + 4x + 1 on the x-axis is_______
4. If the vertex of the parabola y = x & sup2; + (m-2) x + (M & sup2; - 4) is at the origin, then M=________

1. ∵ tell vertex (- 2, - 5)
Let y = a (x + 2) & sup2; - 5
Substituting (1, - 14) into
-14=9a-5
a=-1
∴y=-（x+2）²-5
2. The axis of symmetry is the y-axis
Let y = ax & sup2; - K
Substituting a (1,3) B (- 2, - 6) into
a=-3,k=-6
∴y=-3x²-6
3. The point y = 0 on the x-axis
Let y = 0, the equation can be obtained
-2x²+4x+1=0
x1=2+√6,x2=2-√6
The length of the line cut by the parabola y = - 2x & sup2; + 4x + 1 on the x-axis is 2 √ 6
4. ∵ vertex at origin
∴m-2=0,m²-4=0
To sum up, M = 2

Ask a question about the concept of the third quadratic function
I don't feel very good about this function, y = ax & sup2; + BX + C. when B = 0, the axis of symmetry is y-cycle, but when B is not zero, it has to be converted into vertex form to draw. What is that B for? It doesn't care about the left and right, and it is related to the y-axis? Thank you!

B and a together determine the position of the axis of symmetry of the parabola. For example, both are greater than zero, the axis of symmetry is on the left side of the y-axis, both are less than zero on the left side, one is greater than zero and one is less than zero on the right side

A problem of elementary cubic quadratic function
The image passes through a (1, 0), B (3, 0), C (4, 10)

y=ax^2+bx+c
Substitute a, B, C to solve the equation
y=k(x-1)(x-3) C（4,10）
k=10/3

Ask a question about the concept of the third quadratic function in elementary school
I can't understand the problem of vertex form y = a (X-H) 2
For example: y = 3 (X-5) & sup2; isn't it equal to 3x & sup2; + 75 + 7x? How can this move left and right? Thank you! Online, etc

First of all, y = 3 (X-5) & sup2; is not equal to y = 3x & sup2; + 75 + 7x, it is equal to y = 3x & sup2; - 30x + 75 curve, the vertex of y = 3x & sup2; is at (0,0), because the direction and size of its opening have been determined, the difference is only the vertex coordinates, while the vertex of y = 3 (X-5) & sup2; is (5,0)