Question

What are the vertex and x-intercepts of the graph of y=x2-2x-24

Select one answer for the vertex and one for the x-intercepts

Answer 1

Vertex (1,-25), Intercepts at (6,0) and (-4,0)

Explanation:

Axis of symmetry = -b/2a = -(-2)/2(1) = 2/2 = 1 so x=1 is the equation of line

Plug x=1 into equation y=1-2-24=-25

factor for x-intercepts: (x-6)(x+4)

set them equal to zero: x-6=0 so x=6 x+4=0 so x= - 4

Answer 2

The vertex of the provided equation (1,-25)

The x intercepts are (-4,0) and (6,0).

Explanation:

Consider the provided equation.

`y=x^2-2x-24`

Substitute y=0 to find x intercepts.

`x^2-2x-24=0`

The above equation can be written as:

`x^2+4x-6x-24=0`

`x(x+4)-6(x+4)=0`

`(x+4)(x-6)=0`

By zero product rule:If ab=0 then either a=0 or b=0

`x+4=0` or
`x-6=0`

`x=-4` or
`x=6`

Hence, the x intercepts are (-4,0) and (6,0).

If the equation is in the standard form
`y=a^2+bx+c` then the expression
`(-b)/(2a)` gives the x coordinate of the vertex.

By comparing the provided equation with standard form we can concluded that: a=1, b=-2 and c=-24

Substitute the respective values in the expression
`(-b)/(2a)` we get x coordinates of the vertex:

`(-(-2))/(2(1))=(2)/(2)=1`

Hence, the value of x=1.

Now substitute the value of x in the provided equation to find the value of y.

`y=(1)^2-2(1)-24`

`y=1-2-24`

`y=-25`

Hence, the vertex of the provided equation (1,-25)