How To Find Equation Of Axis Of Symmetry

Download Article

The graph of a polynomial or function reveals many characteristics that would not be articulate without a visual representation. One of these characteristics is the centrality of symmetry: a vertical line on a graph that splits the graph into ii symmetrical mirror images. Finding the axis of symmetry for a given polynomial is fairly simple.^[ane] There are two bones methods.

1
Check the caste of your polynomial. The caste (or "order") of a polynomial is simply the largest exponent value in the expression.^[2] If the caste of your polynomial is 2 (there is no exponent larger than tenⁱⁱ), you tin can find the axis of symmetry using this method. If the degree of the polynomial is college than two, utilise Method two.
- To illustrate, take, as an example, the polynomial 2xⁱⁱ + 3x – one. This highest exponent present is the x², and so information technology is a 2nd order polynomial, and you can use this first method to find the axis of symmetry.
two
Plug your numbers into the axis of symmetry formula. To summate the centrality of symmetry for a 2nd order polynomial in the class ax^two + bx +c (a parabola), use the basic formula ten = -b / 2a.^[iii]
- In the example higher up, a = ii b = iii, and c = -1. Insert these values into your formula, and you will get:
  x = -3 / 2(2) = -three/4.
Advert
3
Write downward the equation of the centrality of symmetry. The value you calculated with your centrality of symmetry formula is the 10-intercept of the axis of symmetry.
- In the example to a higher place, the axis of symmetry is -three/4.
Advertisement

ane

Cheque the caste of your polynomial. The caste (or "guild") of a polynomial is simply the largest exponent value in the expression. If the degree of your polynomial is ii (there is no exponent larger than 10²), you can detect the axis of symmetry using the formula method above. If the degree of the polynomial is higher than ii, utilise this graphical method.
2

Describe the x- and y- axes. Make ii lines in the shape of a plus sign. The horizontal line is your x-centrality; the vertical line is your y-axis.
3

Number your graph. Marker both axes with numbers at equal intervals. Spacing should exist uniform on both axes.
4

Calculate y = f(x) for every x. Take your polynomial or function and calculate values of f(ten) by putting all values of x into it.
5

Make a graph point for each pair. Yous now take pairs of y = f(x) for every x on the axis. For each (x, y) pair, make a indicate on the graph – vertically on the x-axis and horizontally on the y-axis.
6

Draw the graph of the polynomial. Once you have marked all the graph points, you can connect your dots smoothly to reveal a continuous graph of your polynomial.
7

Expect for the axis of symmetry. Inspect your graph carefully. Look for a point on the axis such that when a line is passed through information technology, the graph splits into 2 equal, mirrored halves.^[4]
eight

Note the axis of symmetry. If you can find a point – call it "b" – on the x-axis that splits the graph into two mirrored halves, then that point, b, is your axis of symmetry.

Advert

Add New Question

Question

What is the centrality of symmetry of f for f(ten)=-2|10+3|-7?

The axis of symmetry is x=-3, because the vertex is at (-3,vii). Information technology is an absolute value graph that faces down.
Question

What is the axis of symmetry in x = -ii(x - 3) + 5?

Because this graph consists of a straight line, it does not have an centrality of symmetry. Axes of symmetry occur with parabolic graphs representing quadratic equations ("2d-caste" polynomials).
Question

What is the centrality of symmetry of f(x) = -ten^2 - 6x + 4?

Every bit explained in the above article, the axis of symmetry of a 2nd-degree polynomial in the form of ax² + bx + c is given by the formula x = -b/2a, which in this case is ten = -(-six) / two(1) = 6/2 = 3. x=three.
Question

How do I discover the vertex?
Question

How do y'all find the axis of symmetry for a hyperbola?

A hyperbola has two axes of symmetry. 1 of them is the line passing through both foci. The other is the perpendicular bisector of the foci.
Question

How exercise I notice a quadratic equation given 2 points and a maximum (max y coordinate)?

Use the vertex course for the quadratic function: y = a(x-h)^ii + k. The value of k is the y-coordinate of the vertex which was given to you equally the max, so substitute that in first. And so use the other two (x,y) pairs to become two equations in ii unknowns, a and h. You can solve the arrangement by solving one equation for a and substituting into the other. But since the equations are quadratic in h, you won't get a unique solution. One solution corresponds to a steep parabola with vertex betwixt the other two given points; the other is a shallow parabola with a vertex is further out.

Ask a Question

200 characters left

Include your electronic mail address to become a message when this question is answered.

Submit

Advertizing

The lengths of your ten- and y- axes should allow the overall shape of the graph to be clearly visible.
Some polynomials are non symmetrical. For example, y = 3x has no axis of symmetry.
The symmetry of a polynomial can be classified into fifty-fifty or odd symmetry. Whatever graph that has an axis of symmetry on the y-axis has an "even" symmetry; any graph that has an centrality of symmetry on the x-axis is "odd."

Thanks for submitting a tip for review!

Well-nigh This Commodity

Article Summary X

To find an axis of symmetry, start by checking the caste or largest exponential value of the polynomial. If the degree of your polynomial is ii, you can find the axis of symmetry by plugging the numbers straight into the axis of symmetry formula. Solve the formula and the answer you lot get is the x-intercept of the axis of symmetry. If the degree of the polynomial is higher than 2, you will need to discover the centrality of symmetry by using a graph. For tips on solving graphically, read on!

Did this summary help you?

Thanks to all authors for creating a page that has been read 80,618 times.