A parabola opening up or down has vertex of (0,0) and passes through (4,2). Write it’s equation in vertex form.

Given:

Given that a parabola opening up or down has vertex of (0,0) and passes through the point (4,2).

We need to determine the equation of parabola in vertex form.

Equation of the parabola:

The general form to write the equation of the parabola in vertex form is given by

where (h,k) is the vertex and a is the constant.

Substituting the vertex (0,0) in the above form, we get;

------ (1)

Since, the parabola passes through the point (4,2), let us substitute the point in the above equation.

Thus, we have;

Thus, substituting in equation (1), we get;

Thus, the equation of the parabola in vertex form is

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)