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How do you find the axis of symmetry of a parabola?
How many lines of symmetry does a parabola have?
What are the equations of parabolas with a vertex?
How do you graph a parabola with a vertex other than the origin?
One formula works when the parabola's equation is in vertex form and the other works when the parabola's equation is in standard form . Standard Form. If your equation is in the standard form y = ax2 + bx + c y = a x 2 + b x + c , then the formula for the axis of symmetry is: x = −b 2a x = − b 2 a. Vertex Form.
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...
- Axis of Symmetry Definition
- Standard Form
- Vertex Form
The axis of symmetry is an imaginary line that divides a figure into two identical parts such that each part is a mirror reflection of one another. When the figure is folded along the axis of symmetry, the two identical parts superimpose. A parabolahas one line of symmetry. The axis of the symmetry is the straight line that divides a parabola into ...
The quadratic equation in standard formis, y = ax2+ b x+c where a, b, and c are real numbers. Here, the axis of symmetry formula is: x = - b/2a.
The quadratic equation in vertex form is, y = a (x-h)2 + k where (h, k) is the vertex of the parabola. Here, the axis of symmetry formula is x = h. The axis of symmetry always passes through the vertex of the parabola. Thus identification of the vertex helps us to calculate the position of the axis of symmetry. Axis of symmetry formula for a parabo...
Jun 4, 2023 · The axis of symmetry passes through the vertex (−2, 3) in Figure \(\PageIndex{13}\) and has equation x = −2. Note that the right half of the parabola is a mirror image of its left half across this axis of symmetry. We can use the axis of symmetry to gain an accurate plot of the parabola with minimal plotting of points.
The axis of symmetry of a parabola \(y^2 = 4ax\) is the x-axis, as the x-axis cuts the parabola into two equal halves. What Is The Equation Of Axis Of Symmetry Of Parabola? The axis of symmetry for a parabola \(y^2 = 4ax\) is the x-axis and its equation is y = 0.
Now related to the idea of a vertex is the idea of an axis of symmetry. In general when we're talking about, well not just three, two dimensions but even three dimensions, but especially in two dimensions, you can imagine a line over which you can flip the graph, and so it meets, it folds onto itself.
- 8 min
The equations of parabolas with vertex (0, 0) (0, 0) are y 2 = 4 p x y 2 = 4 p x when the x-axis is the axis of symmetry and x 2 = 4 p y x 2 = 4 p y when the y-axis is the axis of symmetry. These standard forms are given below, along with their general graphs and key features.
