a. Factor the equation:
In this case, the standard form would be more helpful. This is because factoring is easier to do when the equation is in standard form, which is ax^2 + bx + c = 0. The quadratic equation can be factored into two binomial factors, and the standard form allows for easy identification of the coefficients a, b, and c.
b. Graph the parabola:
In this case, the vertex form would be more helpful. The vertex form of a quadratic equation is y = a(x-h)^2 + k, where (h,k) represents the coordinates of the vertex. This form allows for quick identification of the vertex and makes it easier to graph the parabola accurately.
c. Identify the vertex, minimum, or maximum of the parabola:
Again, the vertex form would be more helpful in this task. The vertex form explicitly represents the coordinates of the vertex as (h,k), making it easy to identify the vertex. Additionally, the vertex form also allows for quick identification of the minimum or maximum value of the parabola.
d. Solve the equation using the quadratic formula:
In this case, both forms can be equally helpful. The quadratic formula can be used to solve the equation regardless of whether it is in vertex form or standard form. However, in some cases, the vertex form may provide a simpler expression that can be substituted into the quadratic formula, potentially making the calculations easier.
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.
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1 answer