Draw the graph of the parabola $y = x^{2} + 3 x - 4$ and hence use it to solve $x^{2} + 3 x - 4 = 0$ .
$[5]$

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Solution

We first must find the set of points to be used for the plot.
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Draw the parabola using the points (-4, 0), (-3, -4), (-2, -6), (-1, -6), (0, -4), (1, 0), (2, 6), (3, 14), (4, 24).
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To solve: $x^{2} + 3 x - 4 = 0$ subtract $x^{2} + 3 x - 4 = 0$ from $y = x^{2} + 3 x - 4$ .
$[1]$

The points of intersection of the parabola with the x axis are the points (-4, 0) and (1, 0), whose x – coordinates {-4, 1} is the solution, set for the equation $x^{2} + 3 x - 4 = 0$ .
$[1]$

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(1) Draw the graph of y = x² and y = 2x + 3 and hence solve the equation x² − 2x − 3 = 0.

(2) Draw the graph of y = 2x²and y = 3 − x and hence solve the equation 2x² + x − 3 = 0.

(3) Draw the graph of y = 2x² and y = 3 + x and hence solve the equation 2x² − x − 3 = 0.

D r a w t h e g r a p h o f y = x^{2} + 3 x - 4 a n d h e n c e s o l v e x^{2} + 3 x - 4 = 0 .

y = x^{2} + 3 x + 2

x^{2} + 2 x + 4 = 0

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

y = x^{2} + 3 x + 2

x^{2} + 2 x + 4 = 0

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