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Question

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.

Answer 1

a. Factor the equation:
The standard form would be more helpful for factoring the equation. This is because the standard form, ax^2 + bx + c = 0, clearly shows the coefficients of each term (a, b, and c). By factoring the quadratic equation in standard form, we can easily find its roots by setting each factor equal to zero.

b. Graph the parabola:
The vertex form would be more helpful for graphing the parabola. The vertex form, a(x-h)^2 + k, provides direct information about the vertex of the parabola, which is represented by the values of h and k. By knowing the coordinates of the vertex, it becomes easier to plot the parabola accurately.

c. Identify the vertex, minimum, or maximum of the parabola:
The vertex form would be more helpful for identifying the vertex, minimum, or maximum of the parabola. In the vertex form, a(x-h)^2 + k, the values of h and k represent the coordinates of the vertex. The value of a determines whether the parabola opens upwards or downwards, indicating the maximum or minimum point respectively.

d. Solve the equation using the quadratic formula:
The standard form would be more helpful for solving the equation using the quadratic formula. This is because the quadratic formula, x = (-b ± √(b^2 - 4ac))/2a, directly makes use of the coefficients of the quadratic equation (a, b, and c). By substituting these values into the formula, we can find the solutions to the equation accurately.