Mathematics in the third year of junior high school, ask for expert solutions

The image of the quadratic function intersects below the y-axis and the x-axis, i.e., when x 0; y c 0 error.

Order x 1, obtained from the image; y＜0

i.e.: a b c 0

That's right. The axis of symmetry of this quadratic function is on the positive semi-axis of x and is less than 1, i.e., 0 b 2a 1

0＜﹣b＜2a∴b＜0

b＜02a－b＞0

Mistake. The quadratic function image is open upwards.

So a>0

b^2>0

c<0So: B 2+8A>0>4AC

Correct To sum up, the correct is

Solution: 1. A 0 is obtained from the direction of the opening of the parabola

Knowing from the position of the axis of symmetry of the parabola, 0 -b 2a 1;

b＜2a2a+b＜0。

2. From the parabola and the x-axis have two intersection points, b -4ac 0, and a 0, then 8a 0b -4ac + 8a 0

b²+8a＞4ac。

According to the graph, we can see that a>0 , c<0 , =b -4ac>0 , the axis of symmetry -b 2a>0 so b<0 -b>2a so 2a+b<0a>0 b -4ac>0 so b >4ac , b +8a>4ac just copy this, absolutely correct)

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Solution: y=x(8-x)=8x-x 2=-(x-4) 2+16

Once here, it can be concluded that when x = 4, the value of the equation is the maximum, which is 16

y=x(8-x)=-x^2-8x=-(x-4)^2 +16≤16

When x = 4, y = x (8-x) up to the maximum value of 16 (yuan).

The total profit is y=x(8-x)=-x 2+8x=-(x-4) 2+16 opening down when x=4 has a maximum value y=16When x is equal to 4, the maximum profit is 16 yuan.

The formula for a quadratic equation yields: y= -x-4) 2 +16

Draw: x=4 is the most profitable.

Substituting the two points a and b into y=x +bx+c, get:

0=16-4b+c;

0=9+3b+c.Simultaneous 2 formulas to get the answer b=1; c=6 (if you don't meet the above 2 formulas, shoot out) b=1, c=-12

So the analytic formula for this parabola passing through the points a(-4,0) and b(3,0) is y=x +x-12

The parabola y=x +bx+c, through a(-4,0), b(3,0) two points, the analytic formula of the parabola is.

y=(x+4)(x-3)

Finishing: y=x +x-12

Note that the two points A and B are exactly the two points where the parabola intersects with the x-axis.