Respuesta :

The x intercepts are determide when you calculated the equation when y=0

To find the x-coordinate of the vertex you have to apply the next formula:

[tex]x=-\frac{b}{2a}[/tex]

Where you follow the form of the equation:

[tex]y=ax^2+bx+c[/tex]

X-intercep:

1. In this case if we have the equation in the form: x( x - 2) we can know that y=0 when one of the terms is 0:

y=0 when:

x=0

x-2=0

x= - 2

2. y=0 when:

x-4=0

x=4

x+5=0

x=-5

3. y=0 when:

x-1=0

x=1

x-5=0

x=5x-coordinate of the vertex:

To identify the coeficeints a and b we express the equation in a different form, we have to multiply. Then we can apply the formula to find the x coordinate of the vertex, as follow:

[tex]x=-\frac{b}{2a}[/tex]

1.

[tex]y=x(x-2)=x^2-2x[/tex][tex]x=-\frac{(-2)}{2(1)}=\frac{2}{2}=1[/tex]

2.

[tex]y=(x-4)(x+5)=x^2+5x-4x-20=x^2-x-20[/tex][tex]x=-\frac{(-1)}{2(1)}=\frac{1}{2}[/tex]

3.

[tex]y=(x-1)(x-5)=x^2-5x-x+5=x^2-6x+5[/tex][tex]x=-\frac{(-6)}{2(1)}=\frac{6}{2}=3[/tex]

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