Quadratic function questions: Please help

Let oa=ob=x

Then the coordinates of point A are (x,0) and b is (0,x).

Substituting b(0,x) yields -1 4m 2-1=x and substituting a(-1 4m 2-1,0) yields:

1/4m^2-1)^2+(m+1)(-1/4m^-1)+(1/4m^2-1)=0

1/4m^2-1)(-1/2m^2+m-1)=01/4m^2-1=0

Solution: m= 2;

There is no solution to 0.

m=±2

b is (0,-(1 4)m 2-1).

then a is (-(1 4)m 2-1,0) or ((1 4)m 2+1,0) and a(-1 4m 2-1,0) is substituted into :

1 4m 2-1)(-1 4m 2+m+1)=01 4m 2+m+1=0 solution: m=2 plus or minus 2 times root 2;

Substituting a(1 4m 2+1,0) yields:

1 4m 2+1)(1 4m 2+m+1)=0 solution: m=-2

Because m is an integer, m=-2

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

2 Parabola passes (1, plus or minus 3).

The same shape means a=1

The axis of symmetry x=1 means -b 2a=1 to get b = -2 in substituting (1, plus and minus root number 3) to get two items.

3 Substitute two points.

This results in 2=a+b+c

4+a-b+c

Add the two formulas together.

(1) When 20y>100).

When 60>x>50, y'=100-10(x-50)=600-10x(0x>20)

3) 300>100, then x < 50, substitute y=300 into y=100+10(50-x)=600-10x, and the solution is x=same-day sales profit of 3000 yuan.

It's not a score! You're happy and satisfied! ）

Hello. I don't know how to find me. I guess these questions are from junior high school or high school. Ha ha.. I've been falling behind for a long, long time, and you're supposed to be looking for math, and they're going to give you the answer very quickly, and it doesn't feel like it's that hard.

The hypotenuse is 2x, and the right-angled edge is the root number 2x, so y = half of the square of the root number 2x, i.e. y = x 2, x > 0

1. Sedans do y=x 2-4ax+5a 2-3a=(x-2a) 2+a 2-3a

The minimum value of the quadratic function y=x 2-4ax+5a 2-3a is m, ie.

m=a 2-3a=(a-3 2) 2-9 4, and when a=3 2, the minimum value of m is -9 4.

2, y=-x 2+px+q=-(x-p 2) 2+q+p 2 4, the maximum value of the function y=-x 2+px+q is 16, i.e. q+p 2 4=16, the occlusion balance p 2+4q=64, the image intersects with the x-axis (x1,0)(x2,0), then: x1+x2=p, x1x2=-q.

Therefore |x1-x2|^2=（x1+x2）^2-4x1x2=p^2+4q=64。State bump.

So |x1-x2|=8。

Solution: (1) From the analytic formula, it can be seen that the coordinates of point A are (0,4) (1 minute).

s△oab= 1/2×bo×4=6

bo=3 The coordinates of point b are (-3,0) (2 points).

2) Substituting the coordinates of point b (-3,0) into y=-x2+(k-1)x+4 to obtain -(-3) 2+(k-1) (3)+4=0

The solution is k-1=- 5 3 (4 points).

The analytical formula for the quadratic function is y=-x 2- 5 3x+4 (5 points).

3) Because abp is an isosceles triangle, the coordinates of the point p are (3,0) (6 points) when ab=ap

When ab=bp, the coordinates of the point p are (2,0) or (-8,0) (8 points).

When ap=bp, the coordinates of the point p are (x,0) according to the title, the root number x 2+4 2=|x+3|．

Solution x = 76

The coordinates of point p are (7 6,0) (10 points).

To sum up, the coordinates of point p are (3,0), (2,0), (8,0), (7 6,0).

Solution: The intersection of the image of the quadratic function y=-x 2+(k-1)x+4 with the y-axis at the point a is (0,4), and the point b is (x,0), because.

s aob=6, so -x*4 2=6, so x=-3, so the point b is (-3,0) substituting the quadratic function y=-x 2+(k-1)x+4, and getting 0=-(-3) 2+(k-1)*(3)+4, and the solution is k=-2 3, so the analytical formula of the quadratic function y=-x 2+(k-1)x+4 is.

y=-x^2-5x/3+4;

3.ABP is an isosceles triangle, then AB=AP or AB=BP, so the point P is (3,0) or (2,0).

The function is processed to obtain y=[x+(k-1) 2] 2-(k-1) 2 4+4, and the solution is -3 from the meaning of the question—(k-1) 2 4+4>0

Solve the problem of buying x newspapers.

y=30( (x<=250) max y=750 at this time x=250y=20( (250400).

max y= x=401 at this point

To sum up the above manuscript, 400 copies should be bought every day, and the maximum amount of money earned in a month is 825 yuan.

According to the intersection point a, it can be said that a is substituted into the parabolic analytic equation and the linear analytic equation to obtain an equation about m and a; m,a;

From (1) the expression of the quadratic function can be written; Then determine the opening direction of the parabola according to whether a is greater than 0 or less than 0. Obviously, from (1), we can see that a=-5 and the opening is downward, so when a>0 y decreases with the increase of x.

Hehe! I'm sorry, I can only give you ideas. I can't do it for you. Good for you!

First, the straight line y=2x-3 passes through the point a(m,-1), then -1=2m-3 gives m=1

Then the point a(1,-1) so bring in the parabolic equation and get a=-1

Question 2: y=-x axis of symmetry x=0 opening downward two intervals (-0) increasing (0,+ decreasing.

y=x²-4x+m

x-2)²+m-4

The vertex is on the x-axis, indicating that the maximum or minimum value of y is 0

The minimum value of y=(x-2) +m-4 is when x=2, y(min)=m-4, so m-4=0

m=4y=x -4x+4 The vertex is (2,0)y=(m+6)x-square+2(m-1)x+m+1 To make it always have a focus on the x-axis, then there is always a solution when y=0.

b²-4ac≥0

2(m-1)]²4(m+6)(m+1)≥04m²-8m+4 - 4m²-28m-24≥0-20m-20≥0

m+1≤0m≤-1

The vertex coordinates are (-b 2a, (4ac-b square) 4a), and the vertex on the x-axis means that the vertex ordinate is 0, which gives m=4So the analytic formula is y=x-4x+4The vertex coordinates are (2,0).

（1，0)，（3,0）

That is, the values of the functions are equal when x=1 and x=-3.

So the axis of symmetry x=(1-3) 2=-1

The maximum value is 4, so the vertex is (-1,4).

So it's y=a(x+1) +4

Over (1,0).

0=a(1+1)²+4

a=-1, so y=-x-2x+3

Solution: Let y=ax 2+bx+c, from the title: a<0.

The axis of symmetry of the parabola is x=-b 2a=(-3+1) 2, and we get: b=2a, and the maximum value is (4ac-b 2) 4a=4, c=a+4.

Substituting b,c into the original parabola, and substituting points (1,0) or (-3,0) into the parabola, the following is calculated: a=-1, b=-2, c=3.

Parabolic analytical: y=-x 2-2x+3.