in algebra 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: The standard form of a quadratic equation, ax^2 + bx + c = 0, is generally more helpful for factoring. This is because the factors of the equation can be easily determined by finding the values of x that make the equation equal to zero. The vertex form, on the other hand, may require additional steps to factor the equation.
b. Graph the parabola: The vertex form of a quadratic equation, y = a(x - h)^2 + k, is more beneficial for graphing purposes. This is because the vertex form directly provides the coordinates of the vertex of the parabola (h, k). It also allows for easier identification of the direction and size of the parabola.
c. Identify the vertex, minimum, or maximum of the parabola: Again, the vertex form is more helpful in this scenario. The vertex form directly provides the coordinates of the vertex of the parabola, making it easier to identify the vertex, minimum, or maximum values. The standard form requires additional steps, such as completing the square, to find the vertex.
d. Solve the equation using the quadratic formula: The standard form of a quadratic equation, ax^2 + bx + c = 0, is more beneficial for solving the equation using the quadratic formula. This is because the quadratic formula, x = (-b ± √(b^2 - 4ac))/(2a), is derived from the standard form equation. Substituting the coefficients from the standard form equation into the quadratic formula allows for direct calculation of the roots of the quadratic equation.