Question

What is the benefit of using the factored form of a quadratic? aThe factored form gives the vertex of the parabola bThe factored form gives the minimum of the parabola cThe factored form gives the maximum of the parabola dThe factored form gives the zeros of the parabola

Answer 1

The factored form of a quadratic equation reveals the zeros of the parabola, which are the points where the graph crosses the x-axis. It is often a simpler and more straightforward method than using the quadratic formula, especially when the roots are rational.

Step-by-step explanation:

The benefit of using the factored form of a quadratic equation, ax²+bx+c = 0, is that it reveals the zeros of the parabola. When a quadratic equation is factored, it is expressed as the product of two binomials, (px + q)(rx + s) = 0, where p, q, r, and s are specific numbers that satisfy the original quadratic equation. The zeros of the parabola are the values of x that make each binomial equal to zero and they correspond to the points where the graph of the parabola crosses the x-axis. Solving for x in each binomial gives us the solution of quadratic equations or the roots of the polynomial.

The solution of quadratic equations can also be determined using the quadratic formula, which is derived from completing the square in the general form of a quadratic equation. However, using the factored form is often simpler and more straightforward, especially when the roots are integers or rational numbers.

Answer 2

Quadratic functions f(x) can be written in three forms.

Factored form, the product of a constant and two linear terms:

`a.(x-p).(x-q)\text{ or }a(x-p)^2`

The parameters p and q are the roots of the function (the x-intercepts of the graph y=f(x)). Converting a quadratic function to factored form is called factoring.

Hence, The factored form gives the zeros of the parabola

The correct option is D