Question

What form is best for finding the maximum or minimum of a parabola?

a) Standard form
b) Vertex form
c) Factored form

Answer 1

The vertex form is the best for finding the maximum or minimum of a parabola because it provides the exact coordinates of the vertex, making it easy to identify the parabola's peak or valley.

Step-by-step explanation:

The best form for finding the maximum or minimum of a parabola is the vertex form. The vertex form of a quadratic equation is y = a(x-h)² + k, where the point (h, k) is the vertex of the parabola. This form makes it straightforward to determine the vertex and hence the maximum or minimum point of the parabola, depending on the direction in which it opens.

If the quadratic is currently in standard form (ax²+bx+c=0), you can convert it to vertex form by completing the square or by using the equations h=-b/(2a) and k=c-b²/(4a), where h and k give the x and y coordinates of the vertex, respectively.

In terms of finding the solutions or roots of a quadratic equation, you would use the quadratic formula, which is applicable to the standard form. Factored form is useful for quickly finding the roots when the quadratic can be easily factored, but it doesn't explicitly provide the vertex.