Parabola 1

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Given k(x)= -x^2 + 2x+3, find the coordidnates of the vertex and the equation of the axis of symmetry.
Use the vertex and at least three other points to graph the function.

Solution: This equation k(x)= -x² + 2x+3 is a parabola.

A parabola has the functional form: f(x) = ax² + bx + c with vertex at the point (h , k),

where h = - b / 2a and k = f(h) = c - b 2 / 4

For equation k(x)= -x² + 2x + 3 ,

h = - 2 /( 2*(-1)) = 1

and k = 3 – 4/(4*(-1)) = 3 + 1 = 4

So, the coordinate of vertex = (1, 4)

The equation of the axis of symmetry is x = -b/2a

Hence, x = 1 (putting b = 2 and a = -1)

For equation k(x)= -x² + 2x + 3 , roots are x = -1 and 3

The x intercepts are at the points : (-1 , 0) and (3 , 0).

We get three points (1, 4), (-1 , 0) and (3 , 0), by which we can graph this parabola.