POLYNOMIAL FUNCTIONS 1

my free school tannzania June 16, 2015
POLYNOMIAL FUNCTIONS 1
Problems
Problem : Given the following quadratic function f (x) = 3x 2 - 12x + 13 , decide whether the graph opens upward or downward, find the vertex and axis of the graph, and find any real roots of the function.
The graph opens upward. The vertex is at (2, 1) and the axis is the line x = 2 . It has no real roots.
Problem : Given the following quadratic function f (x) = - 3x 2 - 6x - 3 , decide whether the graph opens upward or downward, find the vertex and axis of the graph, and find any real roots of the function.
The graph opens downward. The vertex is at (- 1, 0) and the axis is the line x = - 1 . It has one real root at x = - 1 .
Problem : Given the following quadratic function f (x) = x 2 - 8x + 19 , decide whether the graph opens upward or downward, find the vertex and axis of the graph, and find any real roots of the function.
The graph opens upward. The vertex is at (4, 3) and the axis is the line x = 4 . It has no real roots.
Problem : Given the following quadratic function f (x) = x 2 , decide whether the graph opens upward or downward, find the vertex and axis of the graph, and find any real roots of the function.
The graph opens upward. The vertex is at (0, 0) and the axis is the line x = 0 . It has one real root at x = 0 .
Problem : Given the following quadratic function f (x) = x 2 - 2x , decide whether the graph opens upward or downward, find the vertex and axis of the graph, and find any real roots of the function.
The graph opens upward. The vertex is at (1, - 1) and the axis is the line x = 1 . It has two real roots, at x = {0, 2} .