How do you write #h= -0.04(d-19)^2 +14.44# in factored form?
The factored form is
The equation as given in the problem statement is in vertex form. Factored form requires knowledge of the roots of the equation. It is easy to get the roots from the vertex form. Simply set the vertex form = 0.
Subtract 14.44 from both sides and divide both sides by -0.04.
Take the square root of both sides.
Add 19 to both sides.
So the two roots are
The factored form of a quadratic equation is
Here, a = -0.04, so in factored form we would have
We can check this algebraically by converting the vertex form and the factored form into the standard form and see if we get the same thing.
CONVERT FROM VERTEX TO STANDARD FORM
CONVERT FROM FACTORED to STANDARD FORM
The standard form is the same, so we have the correct answer.