Knowing the quadratic function y 2x2 4x 3, when 2 x 2, the value range of y is

Knowing the quadratic function y 2x2 4x 3, when 2 x 2, the range of y is analytical: The quadratic function f(x) 2x 2+4x-3=2(x+1) 2-5 When x=-1, f(x) takes the minimum value -5

f(-2)=2(-2+1)^2-5=-3

f(2)=2(2+1)^2-5=13

The value range of y is [-5,13].

The quadratic function can be deformed to y=2(x+1) 2-5

It can be seen that the opening of the quadratic function image is upward, and the function image is the lowest at the point (-1, -5), that is, the function value is the smallest when the function is -1 when xWhen -2 x 2 passes through the lowest point of the image, the minimum value of y is -5

Then look at the maximum maximum value, as long as the endpoint coordinates of the image of 2"x"2 are calculated, compare the size of the function value, and remove the maximum value of the function value.

calculated, when x=-2, y=-3, and x=2, y=13So the maximum value of y is 13

So, the quadratic function y 2x2 4x 3, when 2 x 2, -5 y 13

The graph is a parabola, the opening is upward, so the vertex is the minimum value, which is -b 2a=-1, substituting -1 into the original equation to get the minimum value of y is -5 The greater x on the right side of the parabola, the greater the value of y, when x takes the maximum value of 2, substituting x=2 into the original equation gives the maximum value of y is 13, so the range of y is [-5,13].

It is known that the rotten trap is a subordinated function of the two circles.

y 2x2 4x 3, when 2 x 2, the value range of y is analytical: orange calendar quadratic function f(x) 2x 2+4x-3=2(x+1) 2-5

When x=-1, f(x) takes the minimum value of -5

f(-2)=2(-2+1)^2-5=-3

f(2)=2(2+1)^2-5=13

The value range of y is [-5,13].

y=-2x 2, the parabolic axis of symmetry is delayed by the y-axis, that is, the straight line x=0, the opening is downward, and 1 x 2, x=1, the function y has a maximum value of -2; When x=2, the function y has a minimum value of -8.

i.e. -2 y -8

Therefore, the vertical case of this question is: -2 y -8

In the quadratic function silver fussy y=x 2 -4x-3, a=1 0, the parabolic opening is upward, there is a minimum, y=x 2 -4x-3=(x-2) 2 -7, the symmetrical axis bending of the parabolic front source is x=2, y minimum =-7, -1 x 6, when x=6, y maximum=6 2 -4 6-3=9

7≤y≤9．

So the answer is: -7 y 9

Quadratic function y=x2

In 4x-3, a=1 0, the parabola opening is upward, there is a minimum, and the finch y=x24x-3=(x-2)2

7. The axis of symmetry of the parabola is x=2, and y is the smallest.

7, -1 x 6, when x = 6, y max = 624 6-3 = 9 balance.

7≤y≤9．

So the answer is: -7 y 9

<>y=x22x-1=（x+1）2

Therefore, the answer is: -2 He Fang y Zen Yu Fiber 2

y＝2x²＋8x－3=2（x+2）²-11.

The axis of symmetry is x=-2, and when x=-2, y has a minimum value of -11;

Because of 3 x 3, y has a maximum value of 39 when x=3

The value range of y is -11 y 39

y=-x²+2x+3

x²+2x-1+4

(x²-2x+1)+4

(x-1)²+4

The quadratic term coefficient is -1<0, and the parabolic image is open downward. In the interval [2,+ on the right side of the axis of symmetry, when the function is monotonically decreasing x=2, the maximum value of y is obtained and the range of ymax=-(2-1) +4=3y is (- 3].