Help 1 function in the third year of junior high school, and the problem of the function in the thir

It should be a 2+5b 2+8b

b is the solution of the equation.

So 2b 2 + 4b + 1 = 0

So 2b 2+4b = -1

2(2b^2+4b)=-1*2

4b^2+8b=-2

a, b are 2x 2 + 4x + 1 = 0.

By the Vedic theorem.

a+b=-2,ab=1/2

So a 2 + b 2 = (a + b) 2-2 ab = 4-2 * (1 2) = 3 so a 2 + 5 b 2 + 8b

a^2+b^2)+(4b^2+8b)

A 2+5A 2+8b has a problem, hurry up and add it.

a+b=-2

ab=1/2

a＾2+5b＾2+8b=a＾2+b＾2+4b＾2+8b=(a+b)＾2-2ab+4b(b+2)

a+b=-2

b+2=-a

a＾2+5b＾2+8b=a＾2+b＾2+4b＾2+8b=(a+b)＾2-2ab+4b(b+2)=4-2ab-4ab

4-6ab=4-6*1/2=1

a*b=

a+b=-2

Is the formula behind you written wrong?,A 2+5A 2 isn't 6A 2?

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).

Solution: Let the OABC side length be a then b(a,a) on the image with function y=x(x>0) a=1 a

a=1 Let the edge length of adef be b then e(b+1,b) b=1 (b+1) b=( 5-1) 2

e（√5/2+1/2,√5/2-1/2)

You can let the side length of OABC be a and the side length of fade be b, then a 2=1

a+b)*b=1

So a=1 (1+b)*b=1 b 2+b-1=0 is obtained by the root finding formula of a quadratic equation.

b=(√5-1)/2

Then the coordinates of e are ((5-1) 2+1, (5-1) 2).

Let's solve the first question first:

Let the analytic formula of the parabola be the vertex y=a(x-h) 2+k, because the vertex a(6,8), over o(0,0), h=6,k=8,a=-2 9, i.e., y=[-2(x-6) 2] 9+8=(-2x 2) 9+(8x) 3.

Let's look at the second question:

The abscissa of point D and point C is the same, which is 12, and the ordinate of point D and point A is the same, which is 8, so the coordinate of point D is (12, 8).

The symmetry point of point C with respect to the axis of symmetry is point O, and the analytical formula for the straight line determined by points d and o is y=(2x) 3, and when x=6, y=4. That is, when the coordinates of the P point are (6,4), the circumference of the triangle PDC is minimized.

The third question is to do it again when you have time.

It's too messy.

Solution: 1. When the price is set to be the largest in x, the profit is: y=(30-x)(100-x)=-x 2+130x-3000

For this unary quadratic function, when x=-b (2a), the opening of the parabolic function is taken downwards to the maximum, so the price is x=-130 (-1 2)=65 yuan.

Solution: 2. When a right-angled side is x, the area of the right-angled triangle is the largest, then the side length of another right-angled side is (8-x), and the area of the right-angled triangle is s=x(8-x) 2=-x 2 2+4x

Similarly for such a quadratic function, when x=-b (2a), the opening of the parabolic function is taken as the maximum value downward, so that if one side length is x=-4 (-2 1 2)=4, then the other side length is also 8-4=4 with the largest area, and the maximum area is s=4 4 2=8

1.The pricing should be 65 yuan, the single profit is (x-30), the number of single profit multipliers is the total profit, let y, then y=(x-30)(100-x), is -x 2+130x-3000, this is a one-dimensional quadratic equation, when x is at the axis of symmetry y takes the maximum value, so x=-b 2a=65

2。Let the two right-angled sides of a right-angled triangle be a, b, and a+b=8, from the basic inequality a+b 2ab, ab 4 can be obtained, and the area of the triangle s=1 2ab 2, so the maximum area is 2

Set b1 (m, 2 3m).

2/3m²•√3=m

m=√3/2

a1a=1 set b2(m2,2 3m2).

2/3m2²-1）•√3=m2

m2 = 3 (and one more solution is negative).

a1a2=2

Set b3 (m3, 2 3m3).

2/3m3²-3）•√3=m3

m3 = 3 3 2 (there is one more solution that is negative).

a3a2=3

And so on, a2009a2008=2009

Personally, I think 3 situations should be telling.

Count them one by one! This shouldn't be the third year of junior high school. It should be a senior in high school.

Of course, I don't know if you've learned the concept of proportional sequences? After learning, it can be derived according to the nature of the proportional series.

Of course, it doesn't matter if you haven't studied it. Once this formula is written, the relationship between them can also be observed. Very observable.

You can try it yourself. Believe in your own abilities.

Upstairs, it seems to be non-linear. There must be a transformation of the coordinates to become proportional.

y=ax +bx+c(a 0)over (0,4),(2,-2), to make the parabola in the x-axis the shortest.

Substituting yields 4=c, -2=4a-2b+4

b-2a=3, b=2a+3, a>0, b>3 parabola has the shortest cross-section on the x-axis.

That is, there is only 1 intersection point between the parabola and the x-axis.

That is, b 2-4ac=0,->2a+3) 2=12a to get a=3 2,->b=6

The equation is y=3x2 2+6x+4