Known quadratic function y = - 2x ² How to translate this function image so that it can pass through two points (0,0) and (1,6) Known quadratic function y = - 2x ², How to translate this function image to make it pass through two points (0,0) and (1,6), so that all experts can write a method that can be understood,

Known quadratic function y = - 2x ² How to translate this function image so that it can pass through two points (0,0) and (1,6) Known quadratic function y = - 2x ², How to translate this function image to make it pass through two points (0,0) and (1,6), so that all experts can write a method that can be understood,

After translation, the function becomes: y = - 2 (x + a) ²+ b
It is brought in through points (0,0), (1,6):
-2a ²+ b=0
-2(1+a) ²+ b=6
The solution is a = - 2, B = 8
After translation, the function becomes: y = - 2 (X-2) ²+ eight
That is, first shift the function to the right by 2 units, and then up by 8 units

Set the quadratic function y = X ²- The graph of 2x + 1 shifts up two units and then left three units to obtain the quadratic function y = X ²+ BX + C image, find the values of B and C

y=x^2-2x+1=(x-1)^2
Translate two units up
have to
y-2=(x-1)^2
Shift three units to the left
have to
y-2=(x-1+3)^2=(x+2)^2=x^2+4x+4
y=x^2+4x+6
b=4 c=6

Quadratic function y = - 2x ²- If there are two intersections between X + M-1 and X axis, the value range of M is

△ = bsquare -4ac = 1 + 8 (m-1) > 0
8m>7
m>7/8
Then the value range of M is (7 / 8, + ∞)

Known quadratic function y = x ²+ 2X + C if - 2 < x < 1, the quadratic function has and has only one intersection with the X axis to find the value range of C

If the Y and X axes have 2 intersections, then:
y(-2)=4-4+c=c
y(1)=1+2+c=3+c
Y (- 2) y (1)

Quadratic function y = - x ²+ 2X + 3, if y ≥ 3, the value range of X

If y ≥ 3
Then - x ²+ 2x+3≥3
I.e. - x ²+ 2x≥0
x ²- 2x≤0
x(x-2)≤0
Therefore, the value range of X is 0 ≤ x ≤ 2

In quadratic function y = - x ²+ In the 2x + 1 image, if y increases with the increase of X, what is the value range of X? Explain the content.

The opening of the function is downward
The axis of symmetry is x = 1
On the left side of the symmetry axis, y increases with the increase of X
So the value range of X is X