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Visualising Cartesian System in Two Dimensions

Draw the grap...

Question

Draw the graph of 𝑦=(𝑥−1)(𝑥+3) and hence solve $x^{2} - x - 6 = 0 .$

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Solution

Idea: To solve the quadratic equation, we need to find the equation of the line that cuts the parabola.

$y = (x - 1) (x + 3) = x^{2} - x + 3 x - 3 = 0 y = x^{2} + 2 x - 3$

Draw the parabola using the points (-4, 5), (-3, 0), (-2, -3), (-1,-4), (0, -3), (1, 0), (2, 5), (3, 12), (4, 21)
$W e c a n o b t a i n t h e e q u a t i o n o f a s t r a i g h t l i n e b y s u b t r a c t i n g t h e e q u a t i o n g i v e n t o s o l v e f r o m t h e e q u a t i o n o f p a r a b o l a . T o s o l v e t h e e q u a t i o n x^{2} - x - 6 = 0, s u b t r a c t x^{2} - x - 6 = 0 f r o m y = x^{2} - 2 x - 3$

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}.

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(viii)

(\frac{x}{y} + \frac{y}{z} + \frac{z}{x})^{2}

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Visualising Cartesian System in Two Dimensions

Standard IX Mathematics

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