Grade 10 Simple Quadratic Word Problem Question

[Nathan4102]

Since I missed most of math today, I don't really get the new word problems in the homework. Could someone show me where I go next? I've already partially solved it I think.

Q: Two numbers have a difference of 8. Find the numbers if their product is a minimum.

A:

CODE:

Let x rep the first number let 8 - x rep the second number let y rep the product of the numbers y = (x) (8-x) y = (8x - x?) y = -(x? - 8x + 16) + 16 y = -(x - 4)? + 16

So I've put it in vertex form, which I know he wants us to do, but I'm not sure what to do from here. A bit of help would be awesome!

Nathan

[Dreadnought]

x and 8-x have a difference of eight only when x is 0 or 8

[Nathan4102]

Must be x + 8 then? That would change my equation, but im still not sure where to go from there.

E: In OP, ?'s are exponent 2s.

[Dreadnought]

x + 8 or x - 8 both work

Once you get a parabola find the minimum (I'm assuming you know how to do this part). Congratulations you now know for which x you attain a minimum product. Now you just need to find the other number (x + 8 or x - 8, whichever you chose).

[Nathan4102]

Ohhh ok, I was overthinking it. Thanks!