4H - Solving quadratic simultaneous equations
Solving simultaneous equations involves finding a set of values that satisfies both equations. Graphically, the solution to a set of simultaneous linear equations is the point of intersection when the two, or more, lines/curves are graphed. In this section, we will look at finding the points of intersection between quadratic and linear graphs by solving equations simultaneously.
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■ To solve a quadratic and linear equation simultaneously, it is generally best to get \(y\) as the subject for both equations and then equate the two expressions that are in terms of \(x\). |
The number of solutions, or points of intersection, cab be determined using the discriminant: \(\Delta=b^2-4ac\)
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4H - Example 1: Solving simultaneous equations involving quadratics
Find the point(s) of intersection between \(y=x^2+6x-3\) and \(y=x+3\)
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4H - Example 1: Video solution
4H - Example 1: Practice
Question 1: ABC Question 2: ABC 4H - Example 1: Solutions
Question 1: ABC Question 2: ABC |
4H - Example 2: Using the DISCRIMINANT to find the number of solutions between two functions
Use the discriminant to find when the intersection between \(y=2x^2+2\) and \(y=mx\) will have; no solutions, one solution and two solutions.
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4H - Example 2: Video solution
4H - Example 2: Practice
Question 1: ABC Question 2: ABC 4H - Example 2: 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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Solving quadratic simultaneous equations - Worksheet A
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