If the parabola y x 3 c has a unique common point with the straight line y x 2, then the value of c

In the first step, the two functions of BC are substituted into the analytic formula, and the B coordinates are (3,0) and the C coordinates are (0,3).

The analytic formula is y=-x*2+2x+3

The coordinates of the point p n are (x,-x*2+2x+3) (x,3-x).

According to the formula of the distance between two points in plane geometry, the formula pn=-x*2+2x+3-(3-x)=-(x-3 2)*2+9 4 is the maximum value and the corresponding x value.

Again, according to the equation of the distance between two points in plane geometry, the algebraic formula representing pb pc is listed, and then the equation of pb=pc column is solved, and there is a second-generation back function, and the analytical formula is tested to see whether the p point will be on it, and the abscissa of p is equal to (1-root, number, 13) 2

Finally, the common way to find the area of a triangle in a plane Cartesian coordinate system is to use the plumb height to find its area.

The calculation is inconvenient, and the typing process can be done by yourself according to this idea.

y=x+2 is brought into the parabolic equation.

x²-2x+2-c=0

4+4(c-2)=0

c=1, so choose c

Solution:1When a=b=1, the parabola is: y=3x +2x+c, and when x=1, y=5+c

When x=-1, y=1+c

The axis of symmetry of the parabola is x=-1 3

3.=2 -4 3 c=4-12c>0 c<1 3 The axis of symmetry is x=-1 3 and when -10 1+c<0 or 5+c<0 1+c>0

The value of -5 c is -5

Considering that the ordinate of the parabola vertex coordinates is 4x4c-4=0, c=1 4, the parabola and the x-axis have and only one common point, and the vertex abscissa is x=a2 2x4=a1 4, c=1 4, and there should be only one intersection point between the parabola and the axis of 1 x 1, that is, only one of the intersection points of the parabola and the axis is in the range of [a1,1], and the other is outside this range f(-1)f(1)<0. If f(-1)=2 ten c>o and f(1) = 6 ten c 0 get c> a 2 and c "a 6, there is no solution. f(a1) 0, i.e., 2 ten c 0f(1)>o i.e., 6 ten c>0, get c "one 2 and c a 6, take the intersection one 6c = 1 4 and one 6

Discriminant formula = b 2-4 * (a + c) * 1 4 (a-c) = 0

b^2-a^2+c^2=0

The shape of a triangle with real numbers as the side length is a triangle that is scattered by the spring digging calendar.

Answer: Let y=0, get:

a c x bx a c = 0 with stool.

The parabola has only one common point with the x-axis, indicating that the equation has two equal real roots, and the coarse opening formula of the equation δ=0, b 4 a c a c stupid = 0, and obtains: b c = a , which is obtained from the inverse theorem of the Pythagorean theorem:

The three sides of a, b, and c are right angles.

b^2-(a+c)(a-c)=0 b^2-a^2+c^2=0 a^2=b^2+c^2

It is a right-angled triangle with a as the hypotenuse.

The parabola y=(a+c)x +bx+1 4(a-c) has a unique common point with the x-axis.

Then there is only one solution to the root of the equation (a+c)x +bx+1 4(a-c)=0.

That is, δ = b 4 (a + c) 1 4 (a-c) = 0 to get b c a, so the triangle is a right-angled Bu Zhengxiao triangle containing shape.

b 2-(a-c)*(a+c)=0 (the equation has a line to know that the solution is equal to 0), then b 2+c 2+a 2, so the triangle is a right-angled band.

(1) The x-coefficient is positive, and the parabolic opening is upwards If there is no intersection with the x-axis, then x2 + x+c = 0 has no real solution, and its discriminant formula = 1-2c <0, c > 1 2

2) c is the slope of the straight line y = cx+1, 1 is the intercept on the y axis, both are positive, then the straight line crosses 1, 2, 3 quadrants.

The parabola is y=(x-3) 2+c-8, the parabola takes x=3 as the axis of symmetry, and there is only one intersection point with the x-axis, so the lowest point of the parabola is on the x-axis, so c-8=0, so c=8

There is only one intersection, then y=0 has only one solution, that is, 6 2-4(c+1)=0, c=8

The parabola y=x 2-x+2c and x-axis have no common point, and the book is the equation x 2-x+2c=0, and there is no real solution b 2-4ac=1-8c<0 c> and Hui Teatong Qiantan 1 8b

c>1 8y=x 2-x+2c =(x-1 2) 2+2c-1 4 From the above formula, it can be seen that the parabola y opens to the stove. If there is no intersection between y and x-axis, then it is said that 2c-1 4>0 is c>1 8

There is no common point, i.e. y=0 without root, =1-8c 0, c 1 8 choose b