① Known function y = 2x ²- 4X + 4 (- 2 ≤ x ≤ 0), find the minimum value of Y ② Given that the real numbers a and B satisfy a + B = 2, find a ²+ b ² Minimum value of ③ Given that the positive integers a and B satisfy a + B = 2, find the root a ²+ b ² Minimum value of

Draw a function image
The vertex coordinates are (1,2), and the opening upward symmetry axis X = 1
① X = 0 y min. min = 4
② a ²+ b ²= 2a ²- 4A + 4 is the same as question ①
A when x = 1 ²+ b ² Min, min 2
③ A and B are positive integers, a = 2-b. only a = 1 and B = 1 are possible

Find the maximum or minimum value of the following function y = X ²- 2x-3 y=-2x ²+ 4x

Former: min. - 4
Latter: max. 2

Function y = 2x ²- 4X + 1, X belongs to the minimum value of [- 4,0], Ymin

The first derivative is equal to 4x-4 and is negative in the interval [- 4,0], so the function decreases monotonically. The maximum value is at x = - 4 and the minimum value is at x = 0
Min. Ymin = 2 * 0 ^ 2-4 * 0 + 1 = 1.0
Programming check:
#include
#include
main()
{
float y,x;
for (x=-4;x

Find the function f (x) = x2−2x+2+ Minimum value of x2 − 4x + 8

f(x)＝
(x−1)2+(0−1)2+
(x − 2) 2 + (0 − 2) 2 can be regarded as the sum of the distances from point C (x, 0) to point a (1,1) and point B (2,2), and be the point a '(1, - 1) symmetrical about the X axis of point a (1,1)
∴f(x)min＝
12+32＝
ten

① Known function y = 2x ²- 4X + 4 (- 2 ≤ x ≤ 0), find the minimum value of Y ② Given that the real numbers a and B satisfy a + B = 2, find a ²+ b ² Minimum value of ③ Given that the positive integers a and B satisfy a + B = 2, find the root a ²+ b ² Minimum value of