4G - Graphing quadratic functions
4G - Content video: Graphing quadratic functions
This video covers the theory and discussion about how to graph quadratic graphs.
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A parabola is the shape of a quadratic function. Recall that quadratics are expressed in three forms:
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Transformations:
The turning point form, \(y=a(x-h)^2+k\), provides the most information about the transformations that have occurred to a parabola.
The turning point form, \(y=a(x-h)^2+k\), provides the most information about the transformations that have occurred to a parabola.
- \(a\) causes a dilation by a factor of \(a\) from the \(x\)-axis.
- If \(a<0\) (negative) the graph is reflected over the \(x\)-axis.
- \(h\) causes a translation of \(h\) units parallel to the \(x\)-axis.
- \(k\) causes a translation of \(k\) units parallel to the \(y\)-axis.
- Dilations
- Reflections
- Translations
Dilations and reflections:
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Horizontal translations:
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Vertical translations:
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Method for graphing quadratics:
The following method will vary depending in the equation you start with.
The following method will vary depending in the equation you start with.
- Find the \(y\)-intercept by letting \(x=0\) and solving for \(y\).
- Find the \(x\)-intercepts (if they exist) by letting \(y=0\) and solving for \(x\). This will involve solving a quadratic equation. Remember, the discriminant can be used to determine how many \(x\)-intercepts exist for the graph.
- Find the turning point. This can be done by completing the square or by finding the axis of symmetry.
- Sketch the parabola so that is approximately passes through the positions identified above.
- Label all key features with their coordinates.
4G - Example 1: Sketching a parabola from turning point form
Sketch the graph of the \(f(x)=(x-4)^2+2\). Clearly label any axial intercepts and the turning point with their coordinates.
■ Please note that \(f(x)\) is another notation for naming and working with functions. It is very similar to \(y=...\) |
4G - Example 1: Video solution
4G - Example 1: Practice
Question 1: ABC Question 2: ABC 4G - Example 1: Solutions
Question 1: ABC Question 2: ABC |
4G - Example 2: Sketching a parabola from factorised form
Sketch the graph of the \(f(x)=2(2x-5)(x+1)\). Clearly label any axial intercepts and the turning point with their coordinates.
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4G - Example 2: Video solution
4G - Example 2: Practice
Question 1: ABC Question 2: ABC 4G - Example 2: Solutions
Question 1: ABC Question 2: ABC |
4G - Example 3: Sketching a parabola from general form
Sketch the graph of the \(f(x)=-x^2+5x-4\). Clearly label any axial intercepts and the turning point with their coordinates.
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4G - Example 3: Video solution
4G - Example 3: Practice
Question 1: ABC Question 2: ABC 4G - Example 3: Solutions
Question 1: ABC Question 2: ABC |
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Additional Exercises
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Topic Worksheets
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Other Resources
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Graphing quadratic functions - Worksheet A
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