Find the vertex of the parabola by applying the vertex formula. $$ f(x)=3 x^{2}-18 x+30 $$

Question

UpStudy AI · Accepted Answer

1. Identify the coefficients:  
   $$
   a=3, \quad b=-18
   $$

2. Use the vertex formula for a parabola $$ f(x)=ax^2+bx+c $$:
   $$
   x = -\frac{b}{2a}
   $$

3. Substitute the coefficients into the formula:
   $$
   x = -\frac{-18}{2 \cdot 3} = \frac{18}{6} = 3
   $$

4. To find the $$ y $$-coordinate, substitute $$ x=3 $$ back into the function:
   $$
   f(3) = 3(3)^2 - 18(3) + 30
   $$

5. Simplify step by step:
   $$
   f(3) = 3 \times 9 - 54 + 30 = 27 - 54 + 30 = 3
   $$

6. Thus, the vertex of the parabola is:
   $$
   (3, 3)
   $$
The vertex of the parabola is at (3, 3).

Find the vertex of the parabola by applying the vertex formula.