Final answer:
To convert the vertex form into factored form for the given equation, you need to set f(x) equal to 0 and solve for x. Then, factor out the common term and take the square root to find the roots. Finally, express the equation in factored form using the roots.
Step-by-step explanation:
To convert the vertex form into factored form for the given equation f(x) = -0.17(x-0.7)² + 7, we can start by setting f(x) equal to 0 and then solve for x.
To do this, we rearrange the equation as follows: -0.17(x-0.7)² + 7 = 0.
Next, we factor out -0.17 from the equation: -0.17(x-0.7)² = -7.
And finally, we can write the equation in factored form by taking the square root of both sides: (x-0.7) = √(7/0.17). Now we can solve for x and express the factored form as f(x) = -0.17(x-0.7)(x+5.717)(x-7.117).