A quadratic function is expressed in standard form.
a. Explain two different techniques for determining the maximum or minimum value of the function.
b. Is it always possible to use both techniques? Explain.
Answers
Answer:
A) We can identify the minimum or maximum value of a parabola by identifying the y-coordinate of the vertex. You can use a graph to identify the vertex or you can find the minimum or maximum value algebraically by using the formula x = -b / 2a. This formula will give you the x-coordinate of the vertex.
B) Quantitative data is information about quantities, and therefore numbers, and qualitative data is descriptive, and regards phenomenon which can be observed but not measured, such as language.
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Step-by-step explanation:
two different techniques :-
How to Find the Maximum or Minimum Value of a Quadratic Function Easily
For a variety of reasons, you may need to be able to define the maximum or minimum value of a selected quadratic function. You can find the maximum or minimum if your original function is written in general form, , or in standard form, . Finally, you may also wish to use some basic calculus to define the maximum or minimum of any quadratic function.
Method 1 of 3:
Beginning with the General Form of the Function

1
Set up the function in general form. A quadratic function is one that has an  term. It may or may not contain an  term without an exponent. There will be no exponents larger than 2. The general form is . If necessary, combine similar terms and rearrange to set the function in this general form.[1]
For example, suppose you start with . Combine the  terms and the  terms to get the following in general form:


2
Determine the direction of the graph. A quadratic function results in the graph of a parabola. The parabola either opens upward or downward. If , the coefficient of the  term, is positive, then the parabola opens upward. If  is negative, then the parabola opens downward.[2] Look at the following examples:[3]
For ,  so the parabola opens upward.
For ,  so the parabola opens downward.
For ,  so the parabola opens upward.
You can remember this concept by thinking about smiles and frowns. If someone is positive they smile, and if someone is negative, they frown. Similarly, a positive number will have an upward-facing parabola, and a negative number will have a downward-facing parabola.[4]
If the parabola opens upward, you will be finding its minimum value. If the parabola opens downward, you will find its maximum value.
the best method to use, based on the topic and title of the section. For instance, if you're working on the homework in the "Solving by Factoring" section, then you know that you're supposed to solve by factoring. But in the chapter review and on the test, you don't know from which of your textbook's section a particular quadratic has been drawn.