Question

Vertex form vs. standard form vs. factored form - Which form of a quadratic equation is most useful for identifying the vertex?

a) Vertex form
b) Standard form
c) Factored form
d) All forms provide the same information about the vertex

Answer 1

The vertex form of a quadratic equation is the most useful form for identifying the vertex.

Step-by-step explanation:

The vertex form of a quadratic equation is the most useful form for identifying the vertex. The vertex form of a quadratic equation is given by y = a(x - h)^2 + k, where (h,k) represents the coordinates of the vertex. By comparing the equation to this form, you can easily identify the values of h and k and determine the vertex.

For example, if the equation is y = 2(x - 3)^2 + 5, you can see that the vertex is at (3, 5) by comparing it to the vertex form. The standard form and factored form of a quadratic equation do not directly show the coordinates of the vertex, so they are not as useful for identifying the vertex.