Mathematics!! 20 points quadratic function!! Please, heroes! Good can be a plus!!

If you want to see the most light that passes through, then it means that the whole window area is the largest when x is equal to something First of all, if the total length of the material is limited to 15m, then you can write it according to your diagram.

15=2y+6x+2x (x is the radius of the semicircle on the window) Write the above equation as y=15 2-3x-x

Let the window area be s

Then s=xy+ xx (s is equal to the product of x and y plus multiplied by the sum of the squares of x) and substituting y=15 2-3x-x into the equation of s (which can be complicated) to get a binary equation.

Then I don't need to teach the rest

It's really wrong, upstairs is correct)

There is a mistake in Shijiezoo's formula: the circumference of the semicircle is x, not 2x, so 15=2y+6x+ x, i.e. y=(15-6x- x) 2, so s=2xy+( x 2) 2, i.e. s=15x-(6+ 2)x 2

The next step is to find the vertex value of the quadratic function, and you can do the math yourself.

The most light passing through means the largest area.

The semicircle area is x 2 2

The area of the rectangle is 2x*y=2xy

Area s = 2xy + x 2 2

The constraints of x and y are 7x+4y+ x=15y=(15-7x- x) 4=

s=2x*[

x = 15 14, the window area has a maximum.

s = square meters.

Let the gate equation be x =-2p(y-b).

Then the equation passes through (4,0) and (3,4) and is substituted into the equation:

4²=-2p(0-b)①

3²=-2p(4-b)②

Simplification: 8=pb

Simplification: 9=-8p+2pb

Substitute : 9=-8p+2 8

8p=16-9=7

p=7 8 substitution: b=8 p=8 (7 8)=8 8 7=64 7 The equation is: x = -2 7 8 (y-64 7) x =-7 4 (y-64 7).

When x=0, y=64 7

Conclusion: The height of the gate is meters.

1. y=-(x-3) 2, i.e., y=-x 2+6x-92(1) Substituting x=2 into y=-1 32x2+8 gives y= greater than 7, so it can pass safely.

2) Substituting x=4 into y=-1 32x2+8, y= greater than 7So it's safe to pass.

3) Two-way lanes should be limited to 6 meters in height

1.There is only one intersection point with the x-axis: 0=-x 2+bx+c b 2-4c=00=18+3b+c

Solve b and c

24.(1) It can be passed, according to symmetry, when x = 4 = 2, y = 4 + 8 = >7

Therefore, cars can safely pass through this tunnel.

2) It is safe to pass because when x=4, y=16+8=>7

Therefore, cars can safely pass through this tunnel.

3) The answer is not unique, such as the height limit of 7m

1.From the inscription: the image of y=-x 2+bx+c has only one intersection point with the x-axis, and the coordinates are (3,0), we can see that this quadratic function y=(3-x).

y=-x²-6x+9

2.（1）.Parabola Formula I don't understand what it means, you can assume that the truck is traveling from the center line, i.e., 2 meters on the left and right, i.e., x=2 or -2, and you can find out what is his y value at the point of 2 or -2, and if it is greater than 7, it is safe to pass.

2）.With a two-way street, you can also find out if the value y is less than 7 and if it's not less than 7, then it's safe to pass.

3）.When the height limit is a point of x=8 or -8, the minimum value of y is the value of the tunnel height limit.

Solution: (1) y=(210-10x)(50+x-40)=-10x2+110x+2100 (0 x 15 and x is an integer =..)

2)y=-10(

a=-10 0, when x=, y has a maximum.

0 x 15, and x is an integer, when x=5, 50+x=51, y=2400 (yuan); When x=6, 50+x=56, y=2400 (yuan), when the selling price is set at 55 or 56 yuan per piece, the profit per month is the largest, and the maximum monthly profit is 2400 yuan.

3) When y=2200, -10x2+110x+2100=2200, the solution is x1=1, x2=10

When x=1, 50+x=51;When x=10, 50+x=60

When the selling price is set at 51 or 60 yuan per piece, the profit per month is 2,200 yuan.

When the selling price is not less than 51 yuan and not higher than 60 yuan and is an integer, the monthly profit shall not be less than 2,200 yuan (or when the selling price is 51, 52, 53, 54, 55, 56, 57, 58, 59, 60 yuan, the monthly profit shall not be less than 2,200 yuan).

y=(50-40+x)(210-10x)=-10x2+110x+2100

And 50-40+x>0

x>0210-10x>0

x+50≤65

0x=-b 2a=, y is the maximum. But x is an integer, and when x=5 or x=6, ymax=2400

That is, when the price is set at 55 yuan or 56 yuan, the monthly profit is the largest, and the maximum profit is 2400 yuan.

Let y=2200, and the solution is x1=1, x2=10

That is, when the selling price is set at 51 yuan or 60 yuan, the monthly profit is 2,200 yuan.

Therefore, when the selling price is set at an integer of 51 yuan and 60 yuan, the profit is not less than 2,200 yuan.

After the answer, please.

y=-3x+6

Intersection with axes (0,6)(2,0).

The area of the triangle enclosed: s=2*6 2=6

Translate upwards to get y=-3x+6, and calculate the area of the triangle by yourself.

200*144 80=360 Time spent by 200 machines Now the time spent by each machine.

The extra time to build 200 machines is now the time it takes to make each machine = how many machines can be built in the extra time.

Then add the original 200 units.

Let the function equation be y=kx+b

then k = 2m-2

b=m+1 increases with x, so k>0

i.e. 2m-2>0

m>12.When the function image intersects with the y-axis, i.e., x=0, b>0

So when x=0, b=m+1>0

So m>-1

3.The image passes.

One, two, four quadrants.

So there is k<0 and b>0

So 2m-2<0 and m+1>0

m<1 and m>-1

So -1

(1) 2m-2>0, so m>1

2) The intersection point between the function image and the y-axis is (0,m+1), m+1>0,m>-1(3).

The first, second and fourth quadrants have 2m-2>0, m+1>0, and the solution is m>1

y increases as x increases.

2m-2＞0

m 1 is given by m+1 0

m -1 is calculated by the problem that x decreases as y increases, and intersects with the y axis below x.

2m-2＜0

m+1 0 solution gives m 1

The three questions discuss each of the three scenarios. The main consideration is the understanding of the image of the primary function and the values of k and b.

Specific to this question: k=2m-2, b=m+1

1)k>0

2)b>0

3) k<0 and b>0

Do the math yourself.

Mathematics is the study of the relationship between quantities in the real world - Engels. Since mathematical concepts, theories, and methods are derived from reality and abstracted from real-world materials. The mathematical contents are interconnected, full of dialectical relationships of movement changes and unity of opposites.

This correspondence between functions and equations (systems of equations) and inequalities is a true reflection of this dialectical relationship.

1. The relationship between functions and equations.

1) From a relational point of view.

The relation of the primary function is: y=ax+b(a≠0), and the general form of the unary linear equation is: ax+b=0(a≠0). Conversely, the equation can be converted into a function by rewriting the 0 to the right of the general equation of the unary equation with a variable y.

In the same way, the relation of the quadratic function is y=ax2+bx+c(a≠0), and the general form of the unary quadratic equation is ax2+bx+c=0(a≠0). Replace the 0 on the right side of the equation with a variable y and the equation becomes a function.

2) From the image of the function and the solution of the equation.

The image of a function is a straight line, and this line must intersect with the x-axis, and its intersection coordinates are (-,0), that is, when the dependent variable y=0, its independent variable x=-, and the value of this x is the solution of the equation ax+b=0(a≠0), in other words, the solution of the equation ax+b=0(a≠0) is the abscissa of the point that intersects the x-axis in the countless points on the image-line y=ax+b of the corresponding function; The image of the quadratic function is a parabola, and the position relationship between this parabola and the x-axis has three cases: when the parabola has an intersection point with the x-axis, the corresponding equation ax2+bx+c=0(a≠0) has two equal real roots x1=x2=-, when the parabola and the x-axis have two intersection points, the corresponding equation ax2+bx+c=0(a≠0) has two unequal real roots x1=,x2=, and when the parabola and the x-axis have no intersection point, the corresponding equation ax2+bx+c=0(a≠0) has no real root.

This thing is not a matter of one sentence or two sentences.

You add me as a friend, and I promise you to understand.

Steps: First, change the size of the sign to the equal sign. Second, it should be used as a quadratic equation to solve the problem. Third, draw the range of possible values according to the number axis and combine the size to the number. to get the answer.

Opening direction: up, down, up, down, up.

Axis of symmetry: straight line x=5 3 straight line x= straight line x=-10 straight line x=1 2 straight line x=3

Vertex coordinates: (5 3, 2 3) (10, 20) (1 2, -3 4) (3, -16).

2. y=x^2+9 y=2(x+1)^2-23.(1 12,1 12) straight line x=-1 124 a=-1

The dots are substituted for y=ax 2+bx+c

At 0, the opening direction is upward, the axis of symmetry: the straight line x=-b 2a, vertex coordinates: (-b 2a, (4ac-b 2) 4aa<0, the opening direction is downward at 0 axis of symmetry:

Straight line x=-b 2a vertex coordinates: (-b 2a, (4ac-b 2) 4a