Finding the Axis of Symmetry in a Parabola: How to Solve the Problem

In summary, the conversation is about finding the axis of symmetry of a parabola equation and applying it to solve for a specific problem. The answer is x=0, which creates a vertical line. The initial response of -2a/b was a general formula and not specific to this problem.
  • #1
Niaboc67
249
3

Homework Statement


mIK8i4d.png

The Attempt at a Solution



I would guess it is -b/2a but I have gotten this incorrect. Maybe I have to figure out what the parabola equation is and apply it into the axis of symmetry. Assuming that is correct how would I find that?

Thanks[/B]
 
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  • #2
Niaboc67 said:

Homework Statement


mIK8i4d.png

The Attempt at a Solution



I would guess it is -b/2a but I have gotten this incorrect. Maybe I have to figure out what the parabola equation is and apply it into the axis of symmetry. Assuming that is correct how would I find that?

Thanks[/B]

You should be able to guess it like you guessed the other answers. Do you know what axis of symmetry means visually?
 
  • #3
Isn't it the line which divide the parabola into two even parts. So the line that goes directly down the middle.
 
  • #4
Niaboc67 said:
Isn't it the line which divide the parabola into two even parts. So the line that goes directly down the middle.

Right. What is that line?
 
  • #5
Look to be the y-axis itself?
 
  • #6
Niaboc67 said:
Look to be the y-axis itself?

Right again. Now what's an EQUATION for that line?
 
  • #7
Oh I just looked up some information on this and it looks like x=0 would create a completely vertical line. Is this correct?
 
  • #8
Niaboc67 said:
Oh I just looked up some information on this and it looks like x=0 would create a completely vertical line. Is this correct?

Perfectly correct.
 
  • #9
Awesome! Thank you for your assistance!
 
  • #10
I would just like to add that your initial answer, "- 2a/b", makes no sense because there is no "a" and no "b" in the problem! I assume that was a general formula but you were not asked for a general formula, you were asked for an answer specific to this problem.
 

Related to Finding the Axis of Symmetry in a Parabola: How to Solve the Problem

1. What is an axis of symmetry?

An axis of symmetry is an imaginary line that divides an object into two equal halves, where the two halves are mirror images of each other. In other words, if you were to fold the object along the axis of symmetry, the two halves would overlap perfectly.

2. How do you determine the axis of symmetry of a shape?

To determine the axis of symmetry of a shape, you can follow these steps:

  • Identify any lines of symmetry already present in the shape, if applicable.
  • If there are no lines of symmetry, draw a line through the shape that divides it into two equal halves.
  • Check if the two halves are mirror images of each other. If they are, then the line you drew is the axis of symmetry.
  • If the two halves are not mirror images, try drawing another line and repeat the process until you find the axis of symmetry.

3. Why is the axis of symmetry important?

The axis of symmetry is important because it helps us identify and understand the symmetry of shapes. It also helps us make predictions about the properties of the shape, such as its area, perimeter, and other geometric characteristics.

4. Can a shape have more than one axis of symmetry?

Yes, a shape can have more than one axis of symmetry. In fact, there are some shapes that have an infinite number of axes of symmetry, such as a circle. Other shapes, like a rectangle, can have multiple axes of symmetry depending on the orientation of the shape.

5. How is the axis of symmetry related to the concept of balance?

The axis of symmetry is related to balance because it represents a line of symmetry between two equal and opposite halves of a shape. This balance is visually pleasing and can be found in many natural and man-made objects. For example, the human body has an axis of symmetry down the center, which helps us maintain balance and stability.

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