All courses › Foundations of Mathematics › Quadratic function

Quadratic function

A quadratic function $f(x)=ax^2+bx+c$ has a parabola as its graph. If $a>0$ the parabola opens upward with a minimum, and if $a<0$ it opens downward with a maximum.

f(x) = ax^2 + bx + c

quadratic function

x_t = -\frac{b}{2a}

x-coordinate of the vertex V

Symbols

$a$	sets direction (up/down) and width
$x_t$	x-coordinate of the vertex

Example

$f(x)=-2x^2+8x+3$ : $x_t = -\frac{8}{2\cdot(-2)}=2$ , and $f(2)=-8+16+3=11$ . Since $a<0$ , $(2,11)$ is a maximum.

Plug

x_t

back into the function to find the y-coordinate of the vertex.

Practise functions and graphs for free →

← Linear function · Zeros and discriminant →

Part of Foundations of Mathematics: Functions and graphs.