below are suppose the be the questions:
a. factor the equation
b. graph the parabola
c. identify the vertex minimum or maximum of the parabola
d. solve the equation using the quadratic formula
below are the answers:
Vertex form is most helpful for all of these tasks.
Let
.. f(x) = a(x -h) +k ... the function written in vertex form.
a) Factor:
.. (x -h +√(-k/a)) * (x -h -√(-k/a))
b) Graph:
.. It is a graph of y=x^2 with the vertex translated to (h, k) and vertically stretched by a factor of "a".
c) Vertex and Extreme:
.. The vertex is (h, k). It is a maximum if "a" is negative; a minimum otherwise.
d) Solutions:
.. The quadratic formula is based on the notion of completing the square. In vertex form, the square is already completed, so the roots are
.. x = h ± √(-k/a)
