Draw the graph of $y = 2 x^{2} - x - 3$

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Solution

Assign values of $x$ from $- 3$ to $2$ and calculate the corresponding values for $y$ .Then prepare the following table:
$x$ $- 3$ $- 2$ $- 1$ $0$ $1$ $2$
$x^{2}$ $9$ $4$ $1$ $0$ $1$ $4$
$2 x^{2}$ $18$ $8$ $2$ $0$ $2$ $8$
$- x$ $3$ $2$ $1$ $0$ $- 1$ $- 2$
$- 3$ $- 3$ $- 3$ $- 3$ $- 3$ $- 3$ $- 3$
$y = 2 x^{2} - x - 3$ $18$ $7$ $0$ $- 3$ $- 2$ $3$
Plot the points $(- 3, 18), (- 2, 7), (- 1, 0), (0, - 3), (1, - 2)$ and $(2, 3)$ on the graph sheet and join the points by a smooth curve.We get the required graph of the parabola $y = 2 x^{2} - x - 3$

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Draw the graph of $y = 2 x^{2} + 7 x - 9$ .

(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.

y = 2 x^{2}

2 x^{2} + x - 6 = 0

(1) Draw a graph of y = x² and find the value of.

(2) Draw the graph of y = 2x² and find the value of.

(3) Draw the graph of and find the value of.

y = 2 x^{2}

2 x^{2} + x - 6 = 0

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