Write each quadratic function in the form f(x )=a(x −h) ^2+k , find the vertex, and sketch the graph:

Question

Write each quadratic function in the form f(x )=a(x −h)^2 +k , find the vertex, and sketch the graph:

y = − 1/2 x^2 +x+5/2

y=?(?)^2+?

vertex=?,?

Answer 1

y = -(1/2)x^2 + x + 5/2

= -(1/2)(x^2 -2x) + 5/2

= -(1/2)(x -1)^2 + 5/2 +1/2

= (-1/2)(x-1)^2 + 3

vertex = (1,3),

y intercept = 5/2 or (0,5/2)

x intercepts = 1+ or - (-1)sqr(1-4(-1/2)(5/2))

= 1 + or - -sqr6

x intercepts = (1+sqr6, 0) and (1-sqr6)

axis of symmetry: x= 1

it's a downward opening parabola with maximum point = vertex (1,3)