Question

Please answer the question and please explain in simple way

Answer 1

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:

`x=-(b)/(2a)`

Where you follow the form of the equation:

`y=ax^2+bx+c` 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:

`x=-(b)/(2a)`

1.

`y=x(x-2)=x^2-2x`
`x=-((-2))/(2(1))=(2)/(2)=1`

2.

`y=(x-4)(x+5)=x^2+5x-4x-20=x^2-x-20`
`x=-((-1))/(2(1))=(1)/(2)`

3.

`y=(x-1)(x-5)=x^2-5x-x+5=x^2-6x+5`
`x=-((-6))/(2(1))=(6)/(2)=3`