Question

A quadratic equation can be written in vertex form or i n 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

Answer:

a. Standard form

b. Vertex form

c. Vertex form

d. Standard form

Step-by-step explanation:

The vertex form of a quadratic equation is y = a·(x - h)² + k

The standard form of a quadratic equation is y = a·x² + b·x + c

Therefore;

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

Answer 2

The forms of a quadratic equation are the ways the equation can be written.

The tasks and the required forms are:

• Factor the equation - Standard form
• Graph the parabola - Vertex form
• Identify the vertex, minimum or maximum - Vertex form
• Quadratic formula - Standard form

The standard form of a quadratic equation is:

$\mathbf{y =ax^2 + bx + c}$

The above form can be used to calculate the roots of a quadratic equation, using the following quadratic formula

$\mathbf{x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}}$

Also, a quadratic equation can be easily factorized from $\mathbf{y =ax^2 + bx + c}$

This means that, the standard form can be used for (a) and (d)

The vertex form of a quadratic equation is:

$\mathbf{y = a(x - h)^2 + k}$

The above form is used to

• Identify the vertex
• Identify the maximum and the minimum points of a parabola

This means that, the vertex form can be used for (b) and (c)

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