The coming of the third function will be 20, and the coming of the third function will come

According to the meaning of the problem, the coordinates of the two points can be set as a(x,0), b(0,y) is calculated by the equation (function) y=(2 3)x+3 of the straight line, so that y=0, the value of x (i.e., the coordinates of point a), and the value of y (i.e., the coordinates of point b) is obtained by making x=0, and a(-9 2,0), b(0,3)

Let the analytic formula of the parabola (quadratic function) be y=ax 2+bx+c, and substitute the coordinates of a, b, and c(1,1) into the coordinates of the three points to determine the values of the three coefficients in the function formula (solve the system of ternary linear equations), see below

0=(-9/2)^2*a-(9/2)b+c3=c1=a+b+c

I don't understand the specifics.,Please calculate it yourself.。

y=-2/3x+3

x=0,y=3

y=0,x=9/2

So a(9 2,0), b(0,3).

Let the parabola be y=ax 2+bx+c

x=0,y=3

So 3=a*0+b*0+c

c=3 y=ax^2+bx+3

9, 2, 0) and (on this parabola.)

So 0=a*(9 2) 2+b*(9 2)+381a 4+9b 2=-3 (1).

1=a*1^2+b*1+3

a+b=-2 (2)

1) (2) Synthesis.

Get b=-50 21, a=8 21

y=(8/21)x^2-(50/21)x+3=(8/21)(x-25/8)^2-121/168

So vertex (25 8, -121 168).

Axis of symmetry x = 25 8

Solution: First find points A and B.

by y=-2 3x+3

Let x=0 get y=3

Let y=0 get x=9 2

Therefore a(0,3),b(9 2,0).

Let the parabola y=ax 2+bx+c, (where a is not 0) and (1,1) be substituted into the above analytic equation to obtain it.

a=8/21

b=-32/21

c=3 so axis of symmetry: x=-b 2a=2

The vertices are (2, 31, 21).

Solution: It is known that the intersection point of the line y=-2 3x+3 and the two coordinate axes is a, and the parabola of b passes through the point a, b, so a(0,3),b(9 2,0).

Let the parabolic analytic formula be y=ax +bx+c, and substitute a(0,3),b(9 2,0), ().

c=3,a*(9 2) +b*9 2+c=0,a+b+c=1 gives a=8 21,b=-50 21,c=3 parabolic vertices-2a b=8 25,(4ac-b) 4a=-121 168,x=8 25

A and b are (0,3) and (9,2,0) respectively

Let y=ax*x+bx+c bring in the coordinates of the three points:

a+b+c=1

c=381a/4+9b/2+c=0

The vertices are: a=8 21, b=-50 21, c=3 as: (-b 2a, (4ac-b*b 4a)) = (25 8, -121 168).

Axis of symmetry: x=-b 2a=25 8

As shown in the figure, in the plane Cartesian coordinate system, it is known that the points a(-3,6), points b, and c are on the negative and positive semi-axes of the x-axis, respectively, and the lengths of ob and oc are respectively the two roots of the equation x 2-4x+3=0 (ob is less than oc).

1) Find the coordinates of point b and point c

2) If there is m(1,-2) in the plane, d is a point on the line oc, and dmc= bac is satisfied, and the analytic formula of the straight line md is obtained

3) Are there points q and point p in the coordinate plane (point p is on the line ac) so that the quadrilateral with o, p, c, q as vertices is square? If it exists, please write the coordinates of the q point directly; If not, please explain why

Solution: A is the AE x-axis, and E is the vertical foot; The point of crossing m is the mn x-axis, and n is the perpendicular foot.

1) x 2-4x+3=0 is x1 1x2 3

Point B and point C are on the negative and positive semi-axes of the x-axis, respectively, and the ob is less than oc

Therefore: b( 1,0)c(3,0).

2) Because of CE OC OE 6 AE: EAC ACE 45 degrees.

Because CN OC on 2 mn: NMC NCM 45 degree EAC ace

Again: dmc= bac so: eab= nmd so: rt aeb rt mnd

Therefore: ae mn=eb nd therefore: nd 2 3 therefore: d(5 3,0).

Let the analytic formula of the straight line passing through m and d be y=kx+b

Therefore: 5 3k+b=0k+b=-2Therefore: k=3b=-5

Therefore, the analytic formula of the straight line md is: y=3x-5

3) Exists. q（3/2，－3/2）

Reason: Because: ACE 45 passes the O point as OP AC, then: OP PC Therefore: Q can be found

Again: oc 3 so: p(3 2, 3 2), p, q are symmetrical with respect to the x-axis, therefore: q(3 2, 3 2).

1. The Concept of Function and the Three Elements 1. Definition of Function: Let a and b be two non-null number drawback hole sets, if according to some definite correspondence.

to make any number for set A, all have uniquely determined numbers in set bAnd it corresponds, then it is calledis a function from set a to set b, which counts as, where,It's called an independent variableThe range of values a is called the domain of the function; withvalueA value is called a function value, a collection of function valuesThis is called the range of values. Obviously

2. The three elements of the function: define the domain, the value range, and the relationship between the stool and the stool

3. Definition of function equality: If the definition domain of the two functions is the same and the correspondence is completely consistent, we call the two functions equal

4. Representation of functions

(1) analytic method; (2) image method; (3) List method

Solution: y=-(1 2)x 2+(3 2)x+2=-(1 2)[x 2-3x+(3 2) 2-(3 2) 2-4].

1/2)[(x-3/2)^2-25/4];

So vertex coordinates: (3 2, 25 8).

y=-(1/2)(x-3/2+5/2)(x-3/2-5/2)-(1/2)(x+1)(x-4)

So. x1=-1, x2=4。

From the meaning of the title. 1600+100a=1450+100b1450+200b=1600+300a

Then solve the equation.

From b-a=, that is, b=

Substitute b= into a=

b=3 to find the whole process: it can be 1450+200b=2050 or 1600+300a=2050

A: The race is 2050 meters.

Solution: ab=10 from the Pythagorean theorem, and the height on the ab side in abc calculated from the area is: 48 10=

2) Let the high dm of the hypotenuse intersect fg at the point n, and it is easy to obtain that the triangle cgf is similar to cab, so gf ab=cn cm

i.e. gf ab=(, hence gf=(48-10x), so the area of the pool.

s=x(48-10x), so when x=, the maximum area is: 12

3) by 2) in the scheme, f and e are the midpoints respectively, and by the Pythagorean theorem bm=, so be=, therefore.

The tree is located on the edge of the largest rectangular pool. In order to protect the large trees, the area of the pond will be less than 12

The four sides of the descending rectangle can be considered to be built on the right-angled edge, and the length of the ac edge is x, and the BC edge can be obtained according to the similarity.

The length is (, so the area is s=x(, and the maximum value is 12 from the vertices of the quadratic function

Please make your own diagram and analyze it in detail".

ab=√(8x8+6x6)=10

1)h=8x6/10=

2) FG: AB=(H-DG):H solution yields FG=10-25x 12s=x(10-25x 12)=10x-25x 2 12=[144-(5x-12) 2] 12 When 5x-12=0, i.e., x=, the area is the largest.

3) Let the intersection point of the height on the AB edge and the AB edge be O, then Bo= (be:Bo=EF:AO=X:H is solved to be="The tree is on the edge of the largest rectangular pool.

The improvement plan came according to the first floor, and after sending the answer, I found that someone was faster than me, and better than me.

1 All parabolas y=(x-1) 2-4 intersect the x-axis at BC and the vertices of the two points are a(1,-4).

s△bcd=1\2 s△abc

So the distance from d to the x-axis = half of the distance from a to the x-axis.

So the ordinate of point d is 2 or -2

Substitute y=(x-1) 2-4

There are a total of 4 solutions for the coordinates of point d (root number 6+1,2) (-root number 6+1,2) (root number 2+1,-2) (-root number 2+1,-2).

(root number 6+1,2) or (- root number 6+1,2) or (root number 2+1,-2) or (- root number 2+1,-2).

The process is more complicated, and the camera at home is broken again, so I won't talk about it, I'm sorry.

y=-x+3 over (0,3),(3,0), so l over (0,3),(3,0), you can find the round pin stove l: y=x+3, when x=1, y=m=4, the orange is known as k=1*4=4