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 and solve the equation using the quadratic formula

Answer 1

`\huge{\boxed{\text{A) Standard form}}}\\\huge{\boxed{\text{B) Vertex Form}}}\\\huge{\boxed{\text{C) Vertex Form}}}\\\huge{\boxed{\text{D) Standard Form}}}\\`

Explanation:

Vertex form is represented as:
`f(x) = a(x-h)^2+k`, where the vertex of the parabola is (h, k).

Standard form is represented as
`f(x) = ax^2+bx+c`, where a, b, and c are constants.

A) When factoring an equation, the sum of the roots is equal to b and the sum of the roots is equal to c, meaning standard form is the beneficial.

B) When graphing a parabola, vertex form is extremely beneficial, as it provides the vertex of the parabola, and the direction in which it opens. If "a" is positive, the vertex opens upward, while when "a" is negative, the vertex opens downward. As such, graphing is greatly eased with this information.

C) As is evident from the name, vertex form is the best for identifying the vertex of a parabola, as it is explicitly shown via the constants h and k.

D) The quadratic formula directly uses the constants a, b, and c, so working in standard form is more beneficial, as it removes the effort of solving for each constant.

Hope it helps :) and let me know if you want me to elaborate.

Answer 2

a. In order to factor the equation, the vertex form needs to be expanded to the standard form first, to obtain the factors of the equation

b. The parabola is easily graphed with the information on the vertex given in the vertex form of the quadratic equation

c. The vertex, minimum or maximum of the parabola are easily obtained in the vertex form of the quadratic equation

d. The quadratic formula is defined based on the standard form of the quadratic equation