Draw the graph of 𝑦=(𝑥−1)(𝑥+3) and hence solve x2−x−6=0.
Idea: To solve the quadratic equation, we need to find the equation of the line that cuts the parabola.
y = (x – 1)(x + 3) = x2 – x + 3x – 3 = 0 y = x2+ 2x – 3
Draw the parabola using the points (-4, 5), (-3, 0), (-2, -3), (-1,-4), (0, -3), (1, 0), (2, 5), (3, 12), (4, 21)
We can obtain the equation of a straight line by subtracting the equation given to solve from the equation of parabola. To solve the equation x2 – x – 6 = 0, subtract x2 – x – 6 = 0 from y = x2 – 2x – 3
Plotting the points (-2, -3), (-1, 0), (0, 3), (2, 9), we get a straight line.
The points of intersection of the parabola with the straight line gives the roots of the equation.
The co-ordinates of the points of intersection forms the solution set.
∴ Solution {-2, 3}.