Respuesta :
The major advantage is in getting the peak coordinate(vertex's coordinate) of the point of parabola it is representing.
A quadratic expression written as
[tex]ax^2 + bx + c[/tex]
represents the parabola y = [tex]ax^2 + bx + c[/tex] if the plot is being graphed on XY plane.
Most of the times in practical cases, we need to find the coordinate of the peak point of the parabola.
Peak point is interesting because it is the point of the curve from where the one and only since turn in sign of rate of the function occurs.
Let we take a = 1, b = 2 and c = 3 then we have:
[tex]y = x^2 + 2x + 3[/tex]
Its plot is given below.
If we express the quadratic expression to vertex form which is denoted as:
[tex]a(x-h)^2 + k[/tex],
then the coordinates of the peak of the parabola(also called vertex, that's why the name of the form) is (h,k).
For our plotted parabola, the vertex form is given as:
[tex]y = x^2 + 2x + 3\\= x^2 + 2x + 1 + 2\\= (x + 1)^2 + 2\\[/tex]
Thus we have h = -1 and k = 2. Or the coordinates of the vertex of the parabola is (-1,2), as visible in the plot.
Due to such advantages, we use vertex form. Sometimes, vertex form also evaluates root of the quadratic equations but that only happens sometimes.
Learn more here:
https://brainly.com/question/17587262
