If the function y x2 6x 9 is in the interval a, b a b《3 has a maximum value of 9 and a minimum value

a=-2,b=0 This problem uses the maximum and minimum theorems of quadratic functions: For the quadratic function y=ax+bx+c (a 0), when a x b If a b -b 2a [the line x=-b 2a is the axis of symmetry of the quadratic function y=ax+bx+c] then ymin=f(a),ymax=f(b) [min refers to the minimum value, max refers to the maximum value] solution: the function y=-x+6x+9, so -b 2a=-6 [2 (-1)]=3 because a b 3 So ymin=f(a)= -7= -a+6a+9 So a-6a-9=7 a-6a-16=0 (a-8)(a+2)=0 a1=8 (not in line with the topic, rounded), a2=-2 so a= -2 so ymax=f(b)=9=-b+6b+9 so b-6b=0 b1=0, b2=6 (do not fit the topic, drop off) so b=0 To sum up, a=-2, b=0 [I hope it helps you].

From the meaning of the title, it is -b square + 6b + 9 = 9, b square - 6b = 0, b = 0 or 6, because b is less than 3, then b = 0

A square +6a + 9 = -7, a square - 6a - 16 = 0, (a + 2) (a - 8) = 0, a = -2 or 8, because a is less than 3, then a = -2

Note: The axis of symmetry is x=3, so y is maximum when x=b and y is smallest when x=a.

y=-x2-4x+1=-(x^2+4x+4-4)+1=-(x+2)^2+5

Interval [a,b](b> annihilation a>-2).

Therefore, the function in this interval is a Zheng subtraction function.

Therefore, y(b)=-4 and y(a)=4

Namely. (b+2) 2+5=-4,-(a+2) 2+5=4 gives b=1,a=-1

y=（x-2）2

1, the function family is monotonically decreasing on [-1,1], and the minimum value of the roll number or spike of the letter shirt is f(1)=0, so c is selected

a=-2，b=0

In this problem, we need to use the maximum and minimum value theorems of quadratic functions

For the quadratic function y=ax +bx+c (a 0), when a x b.

If a b -b 2a [the straight line x=-b 2a is the axis of symmetry of the quadratic function y=ax +bx+c].

Then ymin=f(a),ymax=f(b) [min refers to the minimum value, max refers to the maximum value].

Solution: The function y=-x +6x+9, so -b 2a=-6 [2 (-1)]=3

Because a b 3

So ymin=f(a)= 7= -a +6a+9, so a -6a-9=7

a²-6a-16=0

a-8)(a+2)=0

a1 = 8 (do not fit the topic, leave it off), a2 = -2

So a= -2

So ymax=f(b)=9=-b +6b+9, so b -6b=0

b1 = 0, b2 = 6 (do not fit the topic, leave it off).

So b=0

In summary, a=-2, b=0

Hope it helps].

Because y=-(x-3)2

18,a b 3, so when x=a, the function obtains the minimum ymin=-7;When x=b, the function obtains the maximum value ymax, which is ?a

6a+9＝?7

b+6b+9 9, solution: a=8 or -2; b = 0 or 6 and then a b 3 to get a = -2;b=0．

So the answer is -2,0

Analysis: It is clear that this is a quadratic function with an axis of symmetry x=3, and it is clear that its opening is facing downwards, so it is an increasing function in the interval (- 3), and because (a solution: max(y)=f(b)=-b +6b+9=9 is solved to b=0 or b=6

b<3

b=0min(y)=-a²+6a+9=-7

The solution yields a=8 or a=-2

Because a<3

The interval between a=-2 satisfies the question is [-2,0].

y=-x²+6x+9

(x-3)²+18

The symmetry axis of the obtainable function is x=3, and since the opening is downward, the function increases monotonically when x<3!

When x=a has a maximum value, we get:

a²+6a+9=9

That is: a -6a = 0

Solution: a=0 or a=6 (rounded).

When x=b has a minimum value, we get:

b²+6b+9=-7

That is: b -6b-16 = 0

Solution: b=-2 or b=8 (rounded).

So we get: a=0, b=-2

The axis of symmetry is x=3

So in the negative infinity to 3 is the monotonic increase range.

i.e. y=-7 when x=a

y=9 at x=b

When x=a, y=-7, a=8 or -2, a=8 is rounded, and when x=b, y=9, b=0 or 6 b=6, rounded up, a=-2, b=0

It is known to be.

a²+6a+9=-7

b²+6b+9=9

The solution shows that a=-2 b does not exist.

y=-(x-3)^2+18

ax=b, the maximum value is 9

Substituting the solution yields a=-2, b=0

The axis of symmetry is x=3

So in the negative infinity to 3 is the monotonic increase range.

i.e. y=-7 when x=a

y=9 at x=b

When x=a, y=-7, a=8 or -2, a=8 is rounded, and when x=b, y=9, b=0 or 6 b=6, rounded up, a=-2, b=0

The function y=-x +6x+9 increases monotonically over the interval [a,b], so -a +6a+9 = -7 ; b²+6b+9 = 9

a = -2 (a = 8 rounded) b = 0 (b = 6 rounded).

f(x) axis of symmetry is 3 and the opening is downward.

Therefore, f(x) increases the function when x<3.

f(a)=-7 -a 2+6x+16=0 a=-2 or 8 (rounded) f(b)=9 -b 2+6b=0 b=0 or 6 (rounded), so a=-2, b=0

Because the interval x [a,b].and ax=0 or x=-6 when the absolute width f(x)=9, i.e. -(x+3) 2+18=-7 ==x=2 or x=-8

Because when Zen grandly has the interval of x>-3, f(x) is a monotonic subtraction function.

When x<-3 intervals, f(x) is a monotonic increasing function.

So the interval [a,b] that satisfies the condition is [0,2] and [-6,-8], so a=0,b=2 or a=-6,b=-8