Sketches of graphs can give the solutions to quadratic equations. Solutions to equations are given where the line crosses y = 0. Note that reading from a graph may only give an approximate answer. If the line does not cross y = 0, there are no solutions. If the line only touches y = 0, then there is only one solution.
Check any answer obtained from a graph by substituting the values from x into the equation and confirm that they equal, or approximate to, zero.
1. Using the graph below, determine the solutions, if any, of the equation x2 - 4x + 8 = 0.
Answer: There are no solutions to the equation.
Because the line does not cut the x-axis, there are no solutions.
2. Using the graph below, determine the solutions, if any, of the equation 3x2 + 4x - 9 = 0. Give your answers to 1 decimal place.
Answer: 1.1 and -2.4
These are the values when the graph cuts y = 0.
Check the answers by substituting into the original equation:
3 x (1.1)2 + 4 x 1.1 - 9 = -0.37, and
3 x (-2.4)2 + 4 x -2.4 - 8 = -0.32.