Simple minimum/maximum question

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If not, this is a line through the vertex of a parabola that divides the parabola into two halves that are mirror images of each other. If you draw a line through the vertex of a parabola, parallel to the y-axis, it will be the line of symmetry. In this case, the vertex is at (5, -6), so the line of symmetry is x= 5. As for "why it is that", that is just the definition of "line of symmetry".
  • #1
DeanBH
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I did a past paper question whereby I carried the answer (X+5)-6 through.

it then asked for the minimum points of the graph y=x^2 + 10x + 19. which is what i made into (X+5)-6.

I know i have to take the +5 and change its sign to -. and that's the minimum of X. and the -6 without change is the minimum of Y.


I just wondered, can anyone explain to me why this is so?


Furthermore, what would I do if it asked for a maximum. I would show an attempt, but i don't even understand why this is a minimum so it's hard for me to find out the maximum.
( this isn't actually a question I'm just interested.)


thanks :P
 
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  • #2
DeanBH said:
I did a past paper question whereby I carried the answer (X+5)-6 through.

it then asked for the minimum points of the graph y=x^2 + 10x + 19. which is what i made into (X+5)-6.
I presume you mean (x+5)2- 6.

I know i have to take the +5 and change its sign to -. and that's the minimum of X. and the -6 without change is the minimum of Y.


I just wondered, can anyone explain to me why this is so?


Furthermore, what would I do if it asked for a maximum. I would show an attempt, but i don't even understand why this is a minimum so it's hard for me to find out the maximum.
( this isn't actually a question I'm just interested.)


thanks :P
A square is never negative. If y= (x- 5)2- 6, It is always "-6 plus something". If x- 5= 0, which is the same as x= 5 (adding 5 to both sides. I cringe when I read somenthing like "take the+ 5 and change its sign to -"!), y= 0- 6= -6. For any other x, x- 5 is non-zero, (x- 6)2 is positive and (x- 5)2- 6 is larger that 6.

If the problem asked for a maximum, there is something wrong with the problem! The graph of y= (x- 5)2- 6 is a parabola that opens upward: its "vertex" is at the lowest point (5, -6). There is no highest point.

However, if the problem were y= -(x- 5)2- 6 (that's the same as y= x2+ 10 x+ 31), then you can argue that when x= 5, y= -02+ 31= 31 but for any other value of x, y= -(a positive number)+ 31 and so is less than 31. In this case, the graph is a parabola that opens downward. (5, 31) is the highest point on the parabola and 31 is the maximum value of y.
 
  • #3
Can anyone tell me how i find the line of symmetry of this curve, and why it is that 8D
 
  • #4
Do you know the definition of "line of symmetry"?
 

1. What is the definition of a simple minimum/maximum question?

A simple minimum/maximum question is a type of question that asks for the smallest or largest value in a given set of data or range of values.

2. How do you identify the simple minimum/maximum value in a dataset?

To identify the simple minimum/maximum value in a dataset, you can arrange the data in ascending or descending order and then select the first or last value, respectively.

3. What is the difference between a simple minimum/maximum question and a complex minimum/maximum question?

A simple minimum/maximum question only asks for the smallest or largest value in a dataset, while a complex minimum/maximum question may involve multiple variables or conditions to determine the minimum or maximum value.

4. What are some common real-world applications of simple minimum/maximum questions?

Simple minimum/maximum questions are commonly used in fields such as statistics, economics, and engineering to analyze data and make decisions based on the minimum or maximum values.

5. Is there a specific formula or method for solving simple minimum/maximum questions?

There is no specific formula, but the general approach is to first identify the type of question (minimum or maximum) and then use appropriate techniques such as sorting or comparing values to find the answer.

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