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) +k , find the vertex, and sketch the graph:

y = −2x^2 +3x-1

y=?(?)^2+?

vertex=?,?

Answer 1

y = -2x^3 +3x -1

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

= -2(x^2 -3/2x+ 9/16) - 1 + 9/8

= -2(x-3/4)^2 + 1/8 vertex = (3/4, 1/8)

It's a downward opening parabola with maximum point = vertex = (3/4,1/8)

y intercept = -1

x intercepts = 3/4 + or - (1/4)sqr(9-8) = 3/4 + or - 1/4 = 1 or 1/2

axis of symmetry: x = 3/4