General functions
Average rate of change from graphs worksheets
Read four function graphs and estimate their average rates of change. Choose linear, quadratic, cubic, sine or exponential curves, with secants and worked answers.
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Graphing quadratic functions worksheets
Graph four quadratic functions in vertex form on blank coordinate grids. Each sheet includes every leading coefficient from −2, −1, 1 and 2, with a separate completed graph key.
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Plot the vertex first. Use the leading coefficient to find matching points at equal horizontal distances, then draw a smooth symmetric parabola inside the grid.
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Start at the vertex. Build both branches.
Each worksheet has four vertex-form quadratics on blank unit grids from −10 to 10. The four equations use leading coefficients −2, −1, 1 and 2 exactly once, so every set compares direction and width.
For y = a(x − h)² + k, plot (h, k) first. Then evaluate matching inputs on either side of x = h. The separate key shows the complete visible parabola and marks its vertex.
Changing the seed produces new integer vertices from −5 to 5 while preserving the four coefficient cases. The visible curve stops exactly at the grid boundary.
Learning objective
What this activity builds
Use the vertex and leading coefficient in vertex form to draw a symmetric parabola accurately.
Worked example
Graph y = −2(x + 1)² + 3.
The vertex is (−1, 3). The graph opens downward and passes through (0, 1) and (−2, 1).
The expression x + 1 is zero at x = −1. A leading coefficient of −2 reflects the parabola downward and doubles each vertical change from the vertex.
Teaching notes
Make the practice count
- Set the expression inside parentheses equal to zero to locate the vertex.
- Use the sign of a to choose whether the graph opens upward or downward.
- Plot points in symmetric pairs around x = h.
- For |a| = 2, move one unit horizontally and two units vertically.
- Stop the visible curve at the grid boundary; the function itself continues.
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Customize the practice
Choose your options, update the preview, then download the exact same pages.
Change the seed for four new vertex-form quadratics, then print the same graphs with a separate answer key.
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