Integrated Math 2 / Unit 3: Quadratic Functions
3.5 Domain, Range and Intercepts
Notes
The domain is the set of allowed inputs and the range is the set of outputs.
- Every quadratic has domain all real numbers.
- The range starts or ends at the vertex $y$-value $k$: $y \geq k$ if it opens up, $y \leq k$ if it opens down.
- The zeros (roots) are the $x$-intercepts, where $f(x) = 0$. A parabola has 0, 1, or 2 of them.
- Example: $y = x^2 - 9$ has zeros $x = \pm 3$ and range $y \geq -9$.
Practice
What is the range of $y = (x - 1)^2 + 3$?
It opens up with minimum value 3 at the vertex $(1, 3)$.
What is the range of $y = -(x + 2)^2 - 1$?
It opens down, so the maximum is $k = -1$.
What are the zeros of $y = x^2 - 9$?
Set $x^2 - 9 = 0$, so $x^2 = 9$ and $x = \pm 3$.
Ready for more? Take the Unit 3 test.