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Quadratic functions

The graph of a quadratic function is a parabola. If $a > 0$ it opens upwards and has a minimum; if $a < 0$ it opens downwards and has a maximum. The line of symmetry passes through the turning point, and the zeros are found with the quadratic formula.

Try it yourself

The quadratic function

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

quadratic function

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

line of symmetry and turning point

Symbols

a,\ b,\ c

coefficients

Example

$f(x) = x^2 - 4x + 1$ : $x = \frac{4}{2\cdot 1} = 2$ and $f(2) = 4 - 8 + 1 = -3$ . The minimum point is $(2, -3)$ .

The sign of

a

decides whether the turning point is a maximum or a minimum.

Practise functions for free →

← Linear functions · Exponential functions →

Part of Mathematics 1T: Functions.