Question

The equations y= -(x+7)(x+4) and y=-(x-(3) are equivalent. How can both x intercepts be determined if the equation y=-(x+7)(x+4) is given

Answer 1

x-intercepts can be found below

Explanation:

The equation:

`y=-(x+7)(x+4)`

Can also be written as:

`y=-1(x+7)(x+4)`

In order to find the x-intercepts, we must set each of the factors equal to 0.

`-1=0`

`x+7=0, x=-7`

`x+4=0, x=-4`

The x-intercepts are:

`(0,0)`

`(-7,0)`

`(-4,0)`

The equation:

`y=-(x-3)`

Can also be written as:

`y=-1(x-3)`

In order to find the x-intercepts, we must set each of the factors equal to 0.

`-1=0`

`x-3=0, x=3`

The x-intercepts are:

`(0,0)`

`(3,0)`

Answer 2

To find the x-intercepts of the equation y = -(x+7)(x+4), we need to set y = 0 and solve for x. So, we have:

0 = -(x+7)(x+4)

This equation will be true if either (x+7) = 0 or (x+4) = 0. Solving each of these equations, we get:

x+7 = 0 => x = -7

x+4 = 0 => x = -4

Therefore, the x-intercepts of the equation y = -(x+7)(x+4) are x = -7 and x = -4.

Now, we know that the equations y = -(x+7)(x+4) and y = -(x-3) are equivalent. This means that they have the same solutions, or the same x-intercepts. So, we can use the x-intercepts we found for the first equation to determine the x-intercepts of the second equation.

To find the x-intercepts of the equation y = -(x-3), we set y = 0 and solve for x:

0 = -(x-3)

This equation will be true if (x-3) = 0, which gives us:

x-3 = 0 => x = 3

Therefore, the x-intercept of the equation y = -(x-3) is x = 3, which is different from the x-intercepts of the equation y = -(x+7)(x+4). This means that the two equations are not equivalent.

Explanation: