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What is an axis of symmetry?
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Learn what is axis of symmetry, how to find it for different shapes and parabolas, and how to use the formula and equation. See examples, diagrams, and FAQs on axis of symmetry.
Learn the meaning of axis of symmetry, a line through a shape that makes each side a mirror image. See how to identify and draw the axis of symmetry of a shape and how it relates to reflection and symmetry.
Aug 3, 2023 · The axis of symmetry is an imaginary line that makes the shape symmetrical about it. In other words, it divides the shape into two halves such that each half is a mirror image of the other. If we fold and unfold an object along the axis of symmetry, the two sides are identical.
If the parabola opens downward like this, the vertex is the topmost point right like that. It's the maximum point. And the axis of symmetry is the line that you could reflect the parabola around, and it's symmetric. So that's the axis of symmetry. That is a reflection of the left-hand side along that axis of symmetry.
- 7 min
- Sal Khan,Monterey Institute for Technology and Education
- I get that the parabola will open upward when a>0 and downward when a<0, but what if a=0?Good question. It is not a parabola anymore if a = 0. It is just a horizonal line because when you multiply the x by zero it is eliminated and your...
- I got lost at 1:54 because idk where the -4 comes from. then we all of a sudden get to y= -2((x-2)^2...x was divisible by -2 as well as the rest of the numbers on that side of the equal sign. So, the -4 is the result of dividing the 8 on the right en...
- I don't get why the formula Sal talks about at 6:40 (`-b/2a`) works. What's the technical proof.Look by using the completing the square method we essentially turn the equation into vertex form which I suppose you know. Then the result seems as...
- how would u get 16 as the maximum point by using the simple and fast formulae?I asked myself the same question, as Sal seems to have more than a little contempt for the "mindless application" method ;p 'Sokay! I do understand...
- At 3:36, Sal said (x-2)^2 is "always positive" but I think it could be zero too. So shouldn't it be ...Yes, it should be "always non-negative".
- I don't understand why he suddenly said x-2=0Well, let's look at 4:22. y = -2(x-2)² + 16 So, how does this tell us where the vertex is? Well, the vertex will be at the point where y is a minim...
- At about 2:25, Sal adds and subtracts four to the equation. Wouldn't he have to add 8 because the 4 ...You're right, maybe you did it the way I did. However, he did the problem differently, since he factored the 8 out, it changed how he had to solve...
Dec 23, 2023 · Axis of Symmetry Definition. The Axis of Symmetry, a term that can often be heard in Geometry and Algebra, is a line that divides a shape or a graph into two mirror-image halves. Each point on one side of the axis has an identical ‘twin’ on the other side.
The axis of symmetry is a line that divides a shape or function into two identical halves as if folding it along that line. It's crucial in quadratic functions, where it's a vertical line passing through the vertex of the parabola. “Axis of symmetry” is also called “line of symmetry”.
Applet. Picture of the axis of symmetry. Every parabola has an axis of symmetry which is the line that divides the graph into two perfect halves. On this page, we will practice drawing the axis on a graph, learning the formula, stating the equation of the axis of symmetry when we know the parabola's equation.
