When solving a quadratic equation of the form [tex]\( ax^2 + bx + c \)[/tex], finding the vertex of the parabola can be crucial. The vertex of a parabola represented by [tex]\( y = ax^2 + bx + c \)[/tex] occurs at the point [tex]\( (h, k) \)[/tex], where [tex]\( h \)[/tex] and [tex]\( k \)[/tex] can be found as follows:
1. The x-coordinate of the vertex [tex]\( h \)[/tex] is given by the formula [tex]\( h = \frac{-b}{2a} \)[/tex].
So, among the options provided:
1. Finding the discriminant (This helps determine the nature of the roots but not the vertex directly).
2. Substituting coefficients into the quadratic formula (This computes the roots of the equation, not the vertex directly).
3. Calculating [tex]\( x=\frac{-b}{2a} \)[/tex] (This directly computes the x-coordinate of the vertex).
4. Factoring the quadratic expression (This is another method to solve for the roots but does not directly pertain to finding the vertex).
Given this information, the step that involves finding the vertex of the parabola is:
- Calculating [tex]\( x=\frac{-b}{2a} \)[/tex]
Therefore, the correct answer is:
Calculating [tex]\( x=\frac{-b}{2a} \)[/tex]
