Question

Найдите точки пересечения графика функции y= с осью абсцисс.

Answer 1

График пересекает ось абсцисс тогда, когда у=0. Приравняем к нулю и найдем корни уравнения
(х+1)²=0            х²-8х+15=0              3-х≠0
х= -1                 D=4                        х≠3
х1= - 1              х2= 3                      х≠3
                        х3= 5
Учитывая ограничение (знаменатель не равен нулю) х ≠3
х1= -1, х2 = 5                        

Answer 2

$y=0$

$\frac{(x+1)^2(x^2-8x+15)}{3-x} =0$

$(x+1)^2(x^2-8x+15)=0 \\ (x+1)^2=0 \\ x+1=0 \\ x_1=-1$

$x^2-8x+15=0 \\ D=b^2-4ac=(-8)^2-4*1*15=64-60=4 \\ \sqrt{D} =2 \\ x_2= \frac{-b+ \sqrt{D} }{2a}= \frac{8+2}{2} =5 \\ x_3= \frac{-b- \sqrt{D} }{2a}= \frac{8-2}{2} =3$

$(-1;0),(5;0)$ - точки пересечения с осью Ох.

Answer 3

Finding Intersections of the Function y=c with the x-Axis

To find the points of intersection of the function y=c with the x-axis, we can set y to 0 and solve for x. This will give us the x-coordinates of the points where the function intersects the x-axis.

The function y=c intersects the x-axis at the points where y=0. Therefore, to find the points of intersection, we can solve the equation y=c=0 for x.

The points of intersection of the function y=c with the x-axis are the x-coordinates where y=0.

Let's solve the equation y=c=0 for x to find the points of intersection.

Solution:

We have the equation y=c=0. Solving for x, we get: c = 0

This means that the function y=c intersects the x-axis at the point (0, 0).

Therefore, the point of intersection of the function y=c with the x-axis is (0, 0).

This is the only point of intersection of the function y=c with the x-axis.

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