STANDARD F.IF.B.4
AI
For a function that models a relationship between two quantities:
i) interpret key features of graphs and tables in terms of the quantities; and
ii) sketch graphs showing key features given a verbal description of the relationship.
Key features include the following: intercepts; zeros; intervals where the function is increasing, decreasing, positive, or negative; maxima, minima; and symmetries. Tasks have a real-world context and are limited to the following functions: linear, quadratic, square root, piece-wise defined (including step and absolute value), and exponential functions of the form f(x)=a(b)x where a>0 and b>0 (b≠1).
AII
For a function that models a relationship between two quantities:
i) interpret key features of graphs and tables in terms of the quantities, and
ii) sketch graphs showing key features given a verbal description of the relationship.
Key features include: intercepts, zeros; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Tasks may involve real-world context and may include polynomial, square root, cube root, exponential, logarithmic, and trigonometric functions.
Maximum and Minimum: . A parabola's vertex represents either the highest (maximum) or lowest (minimum) point on its graph, depending on whether it opens downwards or upwards.
Vertex: . The vertex is the turning point of the parabola, where the parabola changes direction.
Solutions, Roots, and Zeros: . These terms all refer to the points where the parabola intersects the x-axis (i.e., the x-intercepts).
Axis of Symmetry: . The line that bisects the parabola, passing through the vertex.
Discriminant: . The part of the quadratic formula under the square root (b² - 4ac). It determines the number of real solutions (zeros) a parabola has.
Worksheet: F.IF.B.4: Graphing Quadratic Functions 1
Khan Academy Practice: Link
Worksheet: F.IF.C.7: Graphing Quadratic Functions 1
Khan Academy Practice: Link
Graphing Quadratic and Linear Functions