Question

What are the intercepts of `y=2(x-3)(x+5)`?

Answer 1

See below...

Explanation:

We know that the x intercepts of any quadratic is where the roots are `=` to `0`

`therefore` using `2(x-3)(x+5)=0`

`therefore` `x-3 = 0`
`=>` `x=3`

`therefore x+5=0`
`=> x=-5`

As the roots occur at `y=0`, we get the coordinates of intersection on the x axis are `(3,0) , (-5,0)`

Now we need to work out the y intercept (the point where it crosses the y axis). This will always occur at `x=0` always giving coordinates in the form `(0,y)`

`therefore` subbing `x=0` in the equation, we get.

`2(0-3)(0+5)`
`2(-3)(5)=-30`

`therefore` the y intercept is at `(0,-30)`

Answer 2

`y=-30" and "x=-5,3`

Explanation:

`"to find the intercepts, that is where the graph crosses"`
`"the x and y axes"`

`• " let x = 0, in the equation for y-intercept"`

`• " let y = 0, in the equation for x-intercepts"`

`x=0toy=2(-3)(5)=-30larrcolor(red)"y-intercept"`

`y=0to2(x-3)(x+5)=0`

`"equate each factor to zero and solve for x"`

`x-3=0rArrx=3larrcolor(red)"x-intercept"`

`x+5=0rArrx=-5larrcolor(red)"x-intercept"`
graph{2(x-3)(x+5) [-10, 10, -5, 5]}