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Solving Equations using Graphs | Mathematics for Grade 10 PDF Download

How do we use graphs to solve equations?

  • Solutions are always read off the x-axis
  • Solutions of f(x) = 0 are where the graph of y = f(x) cuts the x-axis
  • If given g(x)=0 instead (Q: “by drawing a suitable straight line”) then:
    • Rearrange into f(x) = mx + c and draw the line y = mx + c
    • Solutions are the x-coordinates of where the line crosses the curve

Note:  Solutions may also be called roots

Example: The graph of y = x3 + - 3x - 1 is shown below.
Use the graph to estimate the solutions (to I dp.) of the equation x3 + x2 - 4x = 0.

Solving Equations using Graphs | Mathematics for Grade 10

We are given a different equation to the one plotted so we must rearrange it to f(x) = mx + c.
x3 + x2 - 4x = 0
Add x — 1 to both sides :
x3 + x2 - 3x - 1 = x - 1
Now plot y = mx + c (which is y = x - 1 here) on the graph — this is the solid red line on the graph below.
Solving Equations using Graphs | Mathematics for Grade 10The solutions are the x coordinates of the crossing points so :
x = - 2.6, x = 0, x = 1.6 

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