Find a question 50 of the first three quadratic functions at a high fraction speed

Solution: Let a(x1,0), b(x2,0), get.

c(0,m-1)

x1+x2=2m

Because AC2 + BC2 = AB2

i.e. (oa 2+oc 2) + ob 2 + oc 2) = ab 2 (o is the origin).

x1^2 + m-1)^2 + x2^2 + m-1)^2 = (x1-x2)^2

2(m-1)^2=-2x1x2=4m-4

m-1=0 or m-1=2 i.e. m=1 or m=3 When m=1, x1=0 or x2=0, that is, a or b coincides with the origin, then acb=90° cannot be established, so m=1 is rounded.

To sum up: m=3

Let a(x1,y1), b(x2,y2).

c（0，m－1）

The vectors AC(Y1 M1,X1,X1),BC(X2,Y2 M1) are perpendicular, so the product of the two vectors is 0

y1 m 1)x2 x1(y2 m 1) 0 denotes y1,y2 as the sum and product of x1,x2.

x1＋x2＝2m

x1＊x2＝2－2m

Therefore, the original formula is transformed into the formula of m.

M3 can be solved

Let the coordinates of two x1, x2, c points (0, t), then.

t=m-1 depends on the nature of a right triangle.

x1*x2|=|t|^2；

According to the Vedic theorem there is.

x1*x2=-2(m-1)；

The next step is to solve the equation, hehe, don't say it again, pay attention to the answer to test. m=3

Solution: (1) Let y=ax 2+bx

According to the image, it can be seen.

a+b=13

4a+2b=24

9a+3b=33

The solution yields a=-1 and b=14

So y=-x 2+14x

2) The parabolic nature shows that when x=-b 2a=7, y is the largest, that is, the profit is the largest.

So in the seventh month, the profit was the largest, at 490,000 yuan.

3) According to the parabolic information, it can be seen that when the business reaches the 14th month, it starts to lose money.

However, from a practical point of view, the company's profits may not necessarily change according to the image.

So this speculation is not reliable.

x=0，y=0

x=1, y=13, x=2, y=24, x=3, y=33, let the quadratic function y=ax 2+bx+c

c=0a+b=13

4a+2b=24

9a+3b=33

Solve a=-1, b=14

So y=-x 2+14x

y=-(x-7)^2+49

The profit in the 7th month was the largest, with a maximum of 490,000.

When x=14, y=0, so the 15th month starts to lose money.

Hello landlord:

1) Bring the coordinates of a and c into the parabola expression respectively, and get c=3, b=-4, so the parabola is: y=x 2-4x+3, and the linear ac equation is x 3+y 3=1 according to the truncated moment, so it is y=-x+3(Why does the drawing not correspond to the question, is C (0,3) or (0,3)?)

2) PD has a maximum value, and the expression of the length of PD is denoted as L, then L=(-x+3)-x 2+4x-3=-x 2+3x=-(x-3 2) 2+9 4<=9 4, when x=3 2, take the equal sign, then p(3 2,-3 4).

3) You have to discuss this in two cases, whether to cut the x-axis, or the y-axis, or whether it is possible for both axes to be tangent at the same time. This has to be drawn, the combination of numbers and shapes to understand, I don't have a pen, I'm afraid I can't write, I hope the idea can help you.

It's not difficult, it's not difficult. It's a pity to use a mobile phone. Two functions are easy to find. You will. The second and third questions are all unknowns.

Solution: If the auxiliary line BH PG intersects at point H and CI PF intersects at point I, then it is easy to prove that BHP is similar to PIC and similar to CKbbk=2 and CK=1

ab=2;cd=3, bc=root number 5

Let pg=x, then, 2=ph=x-2

Easy evidence BHP is similar to PIC is similar to CKB, so ck:BK=pi:IC=BH:

hp = 1:2 so bh = 1 2 (x-2), bp = root number 5 2 (x-2) so pc = bc-bp = root number 5 2 (4-x) so pi = 1 2 (4-x).

So pf=pi+if=pi+cd=1 2(4-x)+3=5-1 2x, so s=pf x pg=x(-1 2x+5)=- i 2(x-5) 2+

When x=4, it is obvious that the area is the largest, and the point p coincides with the point c.

Vertex formula, s=

So when t=20, s is the most big=600

Therefore, the Feizhou Yinqiao key machine can only stop 600m after landing.

How do you have time to find a distance? The title is written incorrectly, you.

1.Solve equation (x-5) (x-1) = 0 to get x1 = 5, x2 = 1;

Because m,n is the solution of the equation, and m is because the image of the parabola y=-x +6x+c passes through the points a(m,o),b(o,n), -m 2+6m+c=0, that is, -1 2+6*1+c=0, and the solution is c=5

So the analytic formula is: y=-x +6x-5

2.Knowing that the intersection point of the parabola and the x-axis is c, the coordinates of point c (-x +6x-5=0) can be solved as (5,0).

The parabolic vertex d point is (3,4), and when x takes the axis of symmetry 3, the maximum value of 4 is obtained

The perpendicular line de of the side bc is made at the point d, and the distance from the point outside the line to the straight line can be solved by de=2 (1 2).

Because BC=5*2 (1 2), DE=2 (1 2), so Area=1 2*BC*DE=5

That is, the area of the triangle is 5

The original equation can be written as (x-5)(x-1)=0 solution of x1=5, x2=1;

Because m,n is the solution of the equation, m*m-6m+5=0, n*n-6n+5=0

and the image of the parabola y=-x +6x+c passes through the points a(m,o),b(o,n), so -m*m+6m+c=0, that is, m*m-6m=c; —0*0+6*0+c=n;i.e. n=c;

m*m-6m+5=0 gives m*m-6m=-5, c=n=-5, so the analytical formula is: y=-x +6x-5

I'll be here today, and I'll continue tomorrow.

From "m,n is the real root of the equation x -6x+5=0, and m n" knows m=1, n=5, and substituting them into y=-x +6x+c to know c=5The second question can be solved after drawing.

Room Unit Price Number of rooms occupied Profit.

Increase 10, increase 20 200 48 200*48-20*48

Assume that the price is increased by 10x RMB.

180+10x 50-x (180+10x)(50-x )-20*(50-x)

Let the profit be yy=(180+10x)(50-x)-20*(50-x)=(160+20x)(50-x).

20[-x^2+42x+400]

When x=21, ymax=29*29*20=16820