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 when factoring the equation. This is because the standard form directly displays the coefficients a, b, and c, making it easier to identify the factors.
b. Graph the parabola: The vertex form of a quadratic equation, f(x) = a(x - h)^2 + k, is more beneficial when graphing the parabola. This is because the vertex form gives the coordinates of the vertex, (h, k), and allows for a clear understanding of the vertex's location on the graph.
c. Identify the vertex, minimum, or maximum of the parabola: The vertex form, f(x) = a(x - h)^2 + k, is again more helpful in identifying the vertex, as it provides the coordinates (h, k) directly in the equation. The value of a also indicates whether the parabola opens upward (minimum) or downward (maximum).
d. Solve the equation using the quadratic formula: The standard form, ax^2 + bx + c = 0, is typically more useful when solving the equation using the quadratic formula. This is because the quadratic formula, x = (-b ± √(b^2 - 4ac))/(2a), requires the coefficients a, b, and c to be easily identified and plugged into the formula to find the solutions for x.