Identifying Quadratic Functions
Identify quadratic functions in Grade 9 algebra by recognizing the standard form y=ax²+bx+c with a≠0, the characteristic parabolic graph, and second constant differences in a table of values.
Key Concepts
New Concept The standard form of a quadratic function is $f(x) = ax^2 + bx + c$, where $a, b,$ and $c$ are real numbers and $a \neq 0$. What’s next Next, you’ll learn to identify these functions, graph their characteristic 'parabola' shape, and predict their orientation from the equation alone.
Common Questions
What defines a quadratic function?
A quadratic function has the form y = ax² + bx + c where a ≠ 0. The highest power of the variable is 2. Its graph is a parabola that either opens upward (a > 0) or downward (a < 0).
How can you identify a quadratic function from a table of values?
Calculate the first differences (subtract consecutive y-values) and then second differences (subtract consecutive first differences). If the second differences are constant and nonzero, the function is quadratic.
What distinguishes a quadratic from a linear and an exponential function?
Linear functions have constant first differences and graphs that are straight lines. Quadratics have constant second differences and parabolic graphs. Exponentials have a constant ratio between consecutive terms and show curved, non-parabolic growth.