How do I find verticies & axis of symmetry?

Question

How do I find verticies & axis of symmetry in general?

Also a recommendation in terms of calculator use .. is there an easier way to see all possibilities for domain and range?

Answer 1

I assume this is for quadratics?

The vertex can be found by -b/2a in the eqn: ax^2 + bx + c = 0 and then plugging in that point into the eqn.

the axis of symmetry for a quadratic is the vertical line where the vertex is a point on, so the line is x=-b/2a.

The easiest way to see domain and range is to check for restrictions such as absolute values, division with variable(s) in the denominator, and roots. Like the eqn:

y=3x/(x+1) >>> here the domain is all reals, but x cant equal -1

However graphing on a calculator is still perhaps the best way to see domain and range.

Answer 2

Not all functions have an axis of symmetry. For a parabola
f(x) = ax^2 +bx+c. the axis of symmetry is the line x = -b/2a. If you plug that value of x into f(x) you will get the y- coordinate of the vertex.

Answer 3

Vertices's are the points where the parabola's (I'm assuming your talking about a parabola) minimum or maximum is. The axis of symmetry is a line that splits the parabola in half.

Answer 4

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