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.(4 points)
a. Factor the equation: The standard form would be more helpful in factoring the equation. This is because the standard form, which is written as ax^2 + bx + c = 0, clearly shows the coefficients of the quadratic equation (a, b, and c). These coefficients can be used to factor the quadratic equation easily.
b. Graph the parabola: The vertex form would be more helpful in graphing the parabola. This is because the vertex form, which is written as a(x - h)^2 + k, gives the coordinates of the vertex of the parabola, which are (h, k). By knowing the coordinates of the vertex, it becomes easier to plot the parabola on a graph.
c. Identify the vertex, minimum, or maximum of the parabola: The vertex form would be more helpful in identifying the vertex, minimum, or maximum of the parabola. The vertex form explicitly states the coordinates of the vertex, which is (h, k). Furthermore, the coefficient "a" also tells if the parabola opens upwards (if "a" is positive) or downwards (if "a" is negative), allowing us to identify the minimum or maximum point.
d. Solve the equation using the quadratic formula: The standard form would be more helpful in solving the equation using the quadratic formula. The quadratic formula is derived directly from the standard form of a quadratic equation, and it requires the coefficients of the quadratic equation (a, b, and c) to be plugged into the formula. Therefore, having the equation in standard form is more suitable for using the quadratic formula.