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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:
In this case, the standard form would be more helpful. The standard form of a quadratic equation is written as ax^2 + bx + c = 0, where a, b, and c are constants. This form makes it easier to identify the factors of the equation through factoring or grouping.
b. Graph the parabola:
In this case, the vertex form would be more helpful. The vertex form of a quadratic equation is written as f(x) = a(x-h)^2 + k, where (h, k) represents the vertex of the parabola. This form provides the coordinates of the vertex of the parabola, making it easier to plot and graph.
c. Identify the vertex, minimum, or maximum of the parabola:
Again, the vertex form would be more beneficial. The vertex form directly provides the coordinates of the vertex, allowing for easy identification of the vertex, as well as determining whether it is a minimum or maximum point.
d. Solve the equation using the quadratic formula:
In this case, the standard form would be more helpful. The quadratic formula is derived from the standard form of a quadratic equation, where the formula allows for solving for the roots of the equation. Plugging the values of a, b, and c into the quadratic formula is more straightforward when the equation is in standard form.