Skip over navigation

Polynomial Functions

Problems

Quadratic Functions

Graphing Higher Degree Polynomials

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} .

Follow Us