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.