Algebra 1 / Unit 9: Quadratic Functions and Equations
9.1 Graphing Quadratic Functions
Notes
A quadratic function has the form $f(x) = ax^2 + bx + c$ with $a \ne 0$. Its graph is a U-shaped parabola.
- If $a > 0$ it opens up and has a minimum. If $a < 0$ it opens down and has a maximum.
- The vertex is the turning point. The axis of symmetry is the vertical line through it: $\displaystyle x = -\frac{b}{2a}$.
- The $y$-intercept is $c$. The $x$-intercepts are the zeros (roots).
Practice
Does $f(x) = -2x^2 + 4x + 1$ open up or down?
The sign of $a$ decides.
The axis of symmetry of $y = x^2 - 6x + 5$ is:
$\displaystyle x = -\frac{-6}{2(1)} = 3$.
The vertex of $y = x^2 + 4x - 1$ is:
$\displaystyle x = -\frac{4}{2} = -2$ and $y = 4 - 8 - 1 = -5$.
Ready for more? Take the Unit 9 test.