What is the axis of symmetry and vertex for the graph y=x^2-4x-3?

1 Answer
Apr 10, 2016

Axis of Symmetry at: x=2
Vertex at: (2,-7)

Explanation:

Note: I'll use the terms Turning Point and Vertex interchangeably as they are the same thing.

Let's first have a look at the vertex of the function

Consider the general form of a parabolic function:
y=ax^2+bx+c

If we compare the equation that you have presented:
y=x^2-4x-3

We can see that:
The x^2 coefficient is 1; this implies that a = 1
The x coefficient is -4; this implies that
b = -4
The constant term is -3; this implies that c = 3
Therefore, we can use the formula:
TP_x=-b/(2a)
to determine the x value of the vertex.
Substituting the appropriate values into the formula we get:

TP_x=-(-4/(2*1))

=4/2

=2

Therefore, the x value of the vertex is present at x=2.

Substitute x=2 into the given equation to determine the y value of the vertex.

y=x^2-4x-3
y=2^2-4*2-3
y=-7

Therefore, the y value of the vertex is present at y=-7.

From both the x and y values of the we can determine that the vertex is present at the point (2,-7).

Now let's have a look at the function's Axis of Symmetry:

The axis of symmetry is essentially the x value of the turning point (the vertex) of a parabola.

If we have determined the x value of the turning point as x=2, we can then say that the axis of symmetry of the function is present at x=2.