Parabolas Math Sample
Click each tab to see the equation for a quadratic function written in vertex form. Identify the vertex and determine if the parabola (graph of the function) opens upward or downward, then check your answers.
\(\small\mathsf{ f(x)= -3(x+4)^2+ 6 }\)
\(\small\mathsf{ f(x)= a(x-h)^2+ k }\)
\(\small\mathsf{ f(x)= -3(x+4)^2+ 6 }\)
Vertex is (-4, 6). The parabola opens downward because a is negative (a= -3).
\(\small\mathsf{ f(x)= 2(x-3)^2-12 }\)
\(\small\mathsf{ f(x)= a(x-h)^2+ k }\)
\(\small\mathsf{ f(x)= 2(x-3)^2-12 }\)
Vertex is (3, -12). The parabola opens upward because a is positive (a= 2).
\(\small\mathsf{ f(x)= -4(x-2)^2+5 }\)
\(\small\mathsf{ f(x)= a(x-h)^2+ k }\)
\(\small\mathsf{ f(x)= -4(x-2)^2+5 }\)
Vertex is (2, 5). The parabola opens downward because a is negative (a= -4).
\(\small\mathsf{ f(x)= 3(x+6)^2-4 }\)
\(\small\mathsf{ f(x)= a(x-h)^2+ k }\)
\(\small\mathsf{ f(x)= 3(x+6)^2-4 }\)
Vertex is (-6, 4). The parabola opens upward because a is positive (a= 3).