Interpret Graphs of Quadratic Functions

Interpret Graphs of Quadratic Functions

GCSE(F), GCSE(H),

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.

Examples

1. Using the graph below, determine the solutions, if any, of the equation x2 - 4x + 8 = 0.

graph showing function x squared - 4x + 8

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.

3 x squared + 4x - 8 = 0

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.