Solving and using quadratic equations - Higher
Another way to solve a quadratic equation is to draw its graph.
This is the graph of: y = x2 - 9x + 20
We can use it to solve: x2 - 9x + 20 = 0
The answers are along the x axis where the graph reaches y = 0 (where it crosses the x axis). Using the graph the answers are x = 4 and x = 5. We can also solve this equation by factorising:
This shows that the solutions are x = 4 and x = 5 which matches the answers in the graph above.
A graphical method can be used to find the solution of a quadratic and linear equation. Suppose we want to find the solutions for:
x2 - 9x + 20 = x - 1
One side of this equation is x2 - 9x + 20. We already know what this graph looks like.
The other side of the equation is x - 1. Drawing y = x - 1 on the same graph we get:
We can check this with the following:
x = 3
x = 7
Solve: x2 + x + 2 = 5 – x
First draw the curve y = x2 + x + 2 and the line y = 5 – x.
The solutions are where the curve and line cross. In this case x = -3 and x = 1.
The answers will not usually be whole numbers.
Solve: x2 + 2x + 1 = x + 4
First draw the curve y = x2 + 2x + 1 and the line: y = x + 4.
The solutions are where the curve and line cross. In this case x = -2.3 and x =1.3.
Because these solutions are correct to one decimal place, a check will give numbers that are close but not exactly the same.
x = -2.3
x = 1.3
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