Solving Quadratic Equations using a Graph

Solving Quadratic Equations using a Graph

GCSE(F), GCSE(H),

Graphs can be used to solve quadratic equations. Arrange the equation so that it is equal to zero on one side. Plot the graph as `y` against the function. The solutions can be found where the line crosses the `x`-axis.

Note that there may be 0, 1 or 2 solutions, depending on how many times the graph crosses the axis.

Note that the answer may only be approximate, depending on how accurately the graph is drawn.

Exam Tip: Substitute the values of `x` from the graph and substitute into the original equation to check the accuracy of the measurement.

Examples

1. By drawing a graph, estimate the solutions to the equation `x^2 - 4x - 3 = 0` to one decimal place.

Answer: `x=4.6 text( and ) x= -0.6`

Plot the graph: coordinates are (-2, 9), (-1, 2), (0, -3), (1, -6), (2, -7), (3, -6), (4, -3), (5, 2), (6, 9)

Graph crosses the `y`-axis at 4.6 and -1.6.

2. By drawing a graph, estimate the solutions to `x^2-8x=-16`.

Answer: `x=4` (both roots take the same value)

Rearrange the equation to `x^2-8x+16=0`, and plot the graph as `y=x^2-8x+16`.

Graph touches the `x`-axis at `x=4`.