![]() 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). 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. Depending on the type of quadratic equation we have, we can use various methods to solve it. Quadratic equations have the form ax2 bx c ax2 bx c. 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. 20 Quadratic Equation Examples with Answers. The vertex form is useful because we can see. Some examples of quadratic equation solver equationsolver ( 1 x 1 1 3 x) returns - 1 13 2 - 1 - 13 2 x 2 - 1 x - 1 0 returns -1, the entire definition is taken into account for the calculation of the numerator admits two roots 1 and -1 but the denominator is zero for x 1, 1 can not be the solution of equation. If the equation \(ax^2 bx c = 0 \) has no solutions then the graph does not cross or touch the x-axis. y a(x h)2 k where a, h and k are real numbers and a is not equal to zero. 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. 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 \(a \textless 0 \). All quadratic functions have the same type of curved graphs with a line of symmetry.
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