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. If you need to factor the equation, it would be more helpful to have the quadratic equation in standard form. This is because factoring is typically easier to do when the equation is in the form ax^2 + bx + c = 0.
b. If you need to graph the parabola, it would be more helpful to have the equation in vertex form. This is because the vertex form of a quadratic equation, y = a(x-h)^2 + k, directly provides the vertex (h,k) of the parabola, which makes graphing it much simpler.
c. If you need to identify the vertex, minimum, or maximum of the parabola, having the equation in vertex form would be more beneficial. The vertex form directly gives you the coordinates of the vertex (h,k), as well as the direction of opening and whether the parabola has a minimum or maximum value.
d. If you need to solve the equation using the quadratic formula, it would be more helpful to have the equation in standard form. This is because the quadratic formula is derived from the standard form of a quadratic equation, ax^2 + bx + c = 0, making it easier to substitute the values of a, b, and c into the formula.