A quadratic can be written in both vertex and standard form. Which form would be most helpful for each of the following tasks? Explain why.
1. Finding the vertex of a quadratic: Vertex form is most helpful for finding the vertex of a quadratic. In vertex form, the equation is written as y = a(x-h)^2 + k, where (h, k) represents the vertex of the parabola. By comparing the equation to the vertex form, we can easily identify the vertex.
2. Graphing a quadratic: Vertex form is also most helpful for graphing a quadratic. By identifying the vertex from the equation in vertex form, we can determine the direction and position of the parabola. Additionally, we can easily identify the axis of symmetry, which is the vertical line passing through the vertex of the parabola.
3. Determining the roots of a quadratic: Standard form is most helpful for determining the roots of a quadratic. In standard form, the equation is written as ax^2 + bx + c = 0. The quadratic formula can be directly applied to determine the roots or zeros of the quadratic equation.
Overall, vertex form is most useful when dealing with the graphical aspects of a quadratic, such as finding the vertex or graphing the parabola. On the other hand, standard form is more useful when working with the algebraic aspects of a quadratic, such as determining the roots.