![]() ![]() The roots of the equation \(y = x^2 -x – 4 \) are the x-coordinates where the graph crosses the x-axis, which can be read from the graph: \(x = -1.6 \) and \(x=2.6 \) (1 dp). Algebra Revise Test 1 2 3 4 5 6 Finding the nth term of quadratic sequences - Higher Quadratic sequences are sequences that include an \ (n2\) term. Plot these points and join them with a smooth curve. Exampleĭraw the graph of \(y = x^2 -x – 4 \) and use it to find the roots of the equation to 1 decimal place.ĭraw and complete a table of values to find coordinates of points on the graph. When the graph of \(y = ax^2 + bx + c \) is drawn, the solutions to the equation are the values of the x-coordinates of the points where the graph crosses the x-axis. If the equation \(ax^2 + bx + c = 0 \) has no solutions then the graph does not cross or touch the x-axis. If the equation \(ax^2 + bx + c = 0 \) has just one solution (a repeated root) then the graph just touches the x-axis without crossing it. The (nth) term for a quadratic sequence has a term that contains (x2).Terms of a quadratic sequence can be worked out in the same way. If the graph of the quadratic function \(y = ax^2 + bx + c \) crosses the x-axis, the values of \(x\) at the crossing points are the roots or solutions of the equation \(ax^2 + bx + c = 0 \). Graph of y = ax 2 + bx + c Finding points of intersection Roots of a quadratic equation ax 2 + bx + c = 0 The turning point lies on the line of symmetry. The graph of the quadratic function \(y = ax^2 + bx + c \) has a minimum turning point when \(a \textgreater 0 \) and a maximum turning point when a \(a \textless 0 \). ![]() Please read the guidance notes here, where you will find useful information for running these types of activities with your students. All quadratic functions have the same type of curved graphs with a line of symmetry. This type of activity is known as Practice. ![]()
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