Key Concepts

• Quadratic functions of form $f(x)=ax^2+bx+c$ may be graphed by evaluating the function at various values of the input variable $x$ to find each coordinating output $f(x)$. Plot enough points to obtain the shape of the graph, then draw a smooth curve between them.
• The vertex (the turning point) of the graph of a parabola may be obtained using the formula $\left( -\dfrac{b}{2a}, f\left(-\dfrac{b}{2a}\right)\right)$
• The graph of a quadratic function opens up if the leading coefficient $a$ is positive, and opens down if $a$ is negative.
• Quadratic functions may be used to model various real-life situations such as projectile motion, and used to determine inputs required to maximize or minimize certain outputs in cost or revenue models.

Glossary

projectile motion

(also called parabolic trajectory) a projectile launched or thrown into the air will follow a curved path in the shape of a parabola

quadratic function

a function of form $f(x)=ax^2+bx+c$ whose graph forms a parabola in the real plane

vertex

the turning point of the graph of quadratic function