A quadratic equation can be written in vertex form or in standard form. Sometimes one form is more beneficial than the other. Identify which form would be more helpful if you needed to do each task listed below and explain why.
a. Factor the equation.
b. Graph the parabola.
c. Identify the vertex, minimum, or maximum of the parabola.
d. Solve the equation using the quadratic formula.
a. Factor the equation: It is more beneficial to have the quadratic equation in standard form when factoring it. This is because it is easier to identify the factors of the equation when it is written in the form: ax^2 + bx + c = 0.
b. Graph the parabola: It is more helpful to have the equation in vertex form when graphing the parabola. Vertex form, y = a(x-h)^2 + k, makes it easier to identify the vertex of the parabola, which is essential for graphing the parabola accurately.
c. Identify the vertex, minimum, or maximum of the parabola: Vertex form is more helpful for identifying the vertex, minimum, or maximum of the parabola. The vertex is explicitly given in vertex form as (h, k), making it easier to determine the coordinates of the vertex.
d. Solve the equation using the quadratic formula: Standard form is more beneficial when solving the equation using the quadratic formula. This is because the quadratic formula is derived from the standard form of the quadratic equation, ax^2 + bx + c = 0, so it is easier to plug in the values of a, b, and c into the formula for solving.