You will explore the concept of quadratic functions studying the free fall of a ball and the jump of a skier.
After completing this tutorial, you will be able to complete the following:
An expression or equation is called quadratic if it has a degree of two.
The highest exponent term in the equation or function should have a power of two or an x squared term. If the highest power is a one then we would have a linear equation.
When we look at a table of values for a quadratic function, the pattern is not a linear one where each of the terms follows the same pattern. In a quadratic function, we will see that the pattern is continuing to increase from term to term. In a table of values for a quadratic function, you need to look at the patterns in both the first and second differences. When the second differences follow the same pattern, then you have a quadratic function.
The General Form of a Quadratic Equation is f(x) = ax^2 + bx + c.
This is the general form of a quadratic equation. The a, b, and c are real numbers. Notice it has an x squared term, a linear term, and a constant. The 'a' term cannot be zero because then you would not have the x squared. Either of the other terms could be zero.
A quadratic function is one in which the resulting graph is a parabola.
The graph of a quadratic is going to be a parabola or a "U" shaped graph. It can be pointing upward or downward depending on the leading term or coefficient being positive or negative. A parabola is symmetrical in shape so the one side looks the same as the other side.
The following key vocabulary terms will be used throughout this Activity Object:
axis of symmetry- the line about which a figure is symmetrical (like a mirror).
domain- the set of input values for which a relation/function is defined.
function - a special type of relation in which each element of the domain is paired with exactly one element of the range.
linear relationship - a relationship where the terms are constant and the resulted graph is a line.; it is in the form f(x) = mx +b.
maximum - the highest point on a graph (vertex if the parabola is downward).
minimum - the lowest point on a graph (vertex if the parabola is upward).
parabola - the U-shaped graph of a quadratic function f(x) = ax2 + bx + c, where a ? 0.
quadratic function - a nonlinear function written in general form f(x) = ax2 + bx + c, where a, b, c are real numbers and a ? 0.
range - set of all output values produced by a function.
vertex - the lowest point (minimum) on a parabola opening up or the highest point (maximum) on a parabola opening down; the point at which a parabola and its axis of symmetry intersect.
x-intercept - the x-coordinate of the point where the parabola intersects the x-axis.
y-intercept - the y-coordinate of the point where the parabola intersects the y-axis.
|Approximate Time||30 Minutes|
|Pre-requisite Concepts||Learners should be familiar with the concept of functions and linear functions.|
|Type of Tutorial||Concept Development|
|Key Vocabulary||parabola, quadratic functions, graphing functions|