a. When factoring the quadratic equation, it is generally more beneficial to have it in standard form. The standard form of a quadratic equation is given as ax^2 + bx + c = 0, where a, b, and c are constants. This form allows us to easily identify the coefficients (a, b, and c) of the quadratic equation, which are important in the factoring process. By factoring, we can find the roots (or zeros) of the equation, which are the x-values that make the equation equal to zero.
b. When graphing the parabola, it is more helpful to have the quadratic equation in vertex form. The vertex form of a quadratic equation is given as a(x - h)^2 + k, where (h, k) represents the vertex of the parabola, and a determines the direction and scale of the parabola. Having the equation in vertex form allows us to easily identify the vertex (h, k) of the parabola, which allows us to locate the turning point. It also helps us determine if the parabola opens upwards or downwards.
c. To identify the vertex, minimum, or maximum of the parabola, it is most helpful to have the equation in vertex form. As mentioned earlier, the vertex form of a quadratic equation is given as a(x - h)^2 + k. By identifying the values of h and k, we can directly determine the coordinates of the vertex (h, k). The vertex represents the minimum or maximum point on the parabola, and knowing its coordinates can help determine the direction and shape of the parabola.
d. When solving the equation using the quadratic formula, it is most helpful to have the equation in standard form. The quadratic formula is given as x = (-b ± √(b^2 - 4ac))/2a, which allows us to find the roots of the quadratic equation. By having the equation in standard form, we can easily identify the required coefficients (a, b, and c) needed for the quadratic formula. Plugging these values into the formula allows us to solve for the roots (or zeros) of the equation.