CCSS.Math.Content.HSF-IF.C.7a
The standard
Graph linear and quadratic functions and show intercepts, maxima, and minima.
Common Core State Standards for Mathematics · Analyze functions using different representations
What this standard means
Students need to graph linear and quadratic functions from equations, tables, or context. They should identify and label x-intercepts, y-intercepts, maximums, and minimums when they exist. They also need to connect these features to the equation and to the situation being modeled.
Mastery looks like accurate graphs with clear scale, labeled key points, and correct language about highest or lowest values. Students often mix up x- and y-intercepts, miss the vertex of a quadratic, or draw a parabola with poor symmetry. They may also forget that linear functions do not have a maximum or minimum unless the domain is limited.
Ways to teach it
- Have students use graph paper to graph y=2x-6 and y=x^2-4x+3, then label intercepts and the vertex.
- Ask students to write what the intercepts and vertex mean for a ball height model, h(t)=-16t^2+32t+5.
- Give a two-question exit ticket: graph one linear function and one quadratic function, then label all key features.
- Show a photo of a fountain arc and have students sketch a parabola, marking the starting height, landing point, and maximum height.
Plan a lesson for CCSS.Math.Content.HSF-IF.C.7a
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Related standards
- CCSS.Math.Content.HSF-IF.C.7e
Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.
- CCSS.Math.Content.HSA-REI.C.7
Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.
- CCSS.Math.Content.HSF-LE.A
Construct and compare linear, quadratic, and exponential models and solve problems
- CCSS.Math.Content.HSF-LE.A.2
Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pa...