Question

Determine the vertex of the graph of the quadratic function, f(x) = x^2 - 5x + 29/4.

Answer 1

Given parabola f(x) = y = x^2-5x+29/4

Compare it standard parabola form y = ax^2+bx+c.

a = 1, b = -5, c = 29/4

Axis of symmetry x = -b/2a = 5/2

To find vertex substitute x value in given equation.

y = (5/2)^2-5(5/2)+29/4

y = 25/4-25/2+29/4

y = (25-50+29)/4

y = 4/4

y = 1

Vertex of parabola = (5/2,1) = (2.5,1)

Graph