Finding answers, 20 questions out of 19 in mathematics

A quadratic function has a unique root, which means that the two roots coincide, which is reflected in the image of the function, that is, the parabola has only one intersection point with the x-axis. At this point, =0 in the quadratic function, ie.

2m+3)² 4*m*(m+5) = 0

Solution, m = 9 8

20(1) is known by: 2 -2 2 + c = 14-4 + c = 1, then c = 1

The parabola is y=x-2x + 1=(x-1) and the vertex coordinates of the parabola are (1,0).

2) Let the parabola be y=(x-1) -k and the intersection point of the parabola with the x-axis is a,b

x-1)²-k=0

x-1)²=k

x-1= k, then x=1 k

ab=2|1 + k - 1 - k)|=2|2√k|=2

k=1, then k=1

The parabola is y=(x-1) 1=x -2x

20 (1) is obtained by staring at x=0, y=1: c=1

Substituting x=2, y=1 into the quadratic function:

a 2 +b 2 + 1 = 4a + 2b + 1 = 1 then 4a + 2b = 0, the oak calendar is: b = -2a

In the same way: substituting x=-1 and y=-5 into :

a•(-1)² b•(-1) +1=a-b+1=-5a-b=-6

then a-(-2a)=-6

3a=-6, then a=-2

b=-2a=4

The quadratic function is y=-2x +4x+1

2) From (1): y=-2(x -2x) +1-2(x -2x + 1 - 1) +1-2(x-1) 3

The vertex beam search is (1,3).

When x=4: m=-2 4 +4 4 + 1

1= c, 3= b (two straight lines are parallel and the isotope angles are equal) 2= 4 (two lines are parallel and the internal wrong angles are equal).

4= a (two straight lines are parallel and the angles are equal).

2=∠a∠1=∠c，∠3=∠b

c+∠a+∠b＝∠1+∠2+∠3＝180

1 = c, 3 = b (two parallel lines with equal isotopic angles).

2 = 4 (two straight lines are parallel, and the inner wrong angles are equal).

Question 1: 2+1+2-1-1+2=5

The second question should be used.

19（2）r=6;Proof Questions...

20(2) The median of a class is 35; The number of late shifts is 30

3) 40% of the excellent rate of the first class; The pass rate of the second class is 75%.