Key Concepts

• Quadratic functions of form [latex]f(x)=ax^2+bx+c[/latex] may be graphed by evaluating the function at various values of the input variable [latex]x[/latex] to find each coordinating output [latex]f(x)[/latex]. 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 [latex]\left( -\dfrac{b}{2a}, f\left(-\dfrac{b}{2a}\right)\right)[/latex]
• The graph of a quadratic function opens up if the leading coefficient [latex]a[/latex] is positive, and opens down if [latex]a[/latex] 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 [latex]f(x)=ax^2+bx+c[/latex] whose graph forms a parabola in the real plane

vertex

the turning point of the graph of quadratic function