SOLUTION: Write a quadratic function in standard form with zeros 6 and -8?

Question 548218: Write a quadratic function in standard form with zeros 6 and -8?
Found 2 solutions by nerdybill, mathie123:
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
Write a quadratic function in standard form with zeros 6 and -8?
A zero at 6 means a factor of
(x-6)
A zero at -8 means a factor of
(x+8)
.
the function must then be:
(x-6)(x+8)
x^2+8x-6x-48
x^2+2x-48

Answer by mathie123(224) (Show Source): You can put this solution on YOUR website!
We know if the quadratic function has zeros 6 and -8 then
x-6 and x-(-8)=x+8 are both factors of the quadratic function This means that

Now... standard form is also known as vertex form and is written as

We can expand our quadratic from above and then put it into this form:

Now we must complete the square to get it into standard form. To do this, we must add half of the b value squared ((half of 2 is 1 and 1 squared is 1 so we add one). If we add 1, we must subtract it as well (so we are essentially not changing the equation).

Now taking the first three terms, they can be factored as so:

there we have it:)
Let me know if you are unsure about anything and I will make sure it is clear for you :)

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