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

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Solution

$x$ $- 3$ $- 2$ $- 1$ $0$ $1$ $2$ $3$ $4$ $5$
$- x^{2}$ $9$ $4$ $1$ $0$ $- 1$ $- 4$ $- 9$ $- 16$ $- 25$
$2 x$ $- 6$ $- 4$
$- 2$ $0$ $2$ $4$ $6$ $8$ $10$
$+ 3$ $+ 3$ $+ 3$ $+ 3$ $+ 3$ $+ 3$ $+ 3$ $+ 3$ $+ 3$ $+ 3$
$y = - x^{2} + 2 x + 3$ $- 12$ $- 5$ $0$ $3$ $4$ $3$ $0$ $- 5$ $- 12$
Plot the points $(- 3, - 12), (- 2, - 5), (- 1, 0), (0, 3), (1, 4), (2, 3), (3, 0), (4, - 5)$ and $(5, - 12)$ on the graph sheet and join the points by a smooth curve.We get the required graph of the parabola $y = - x^{2} + 2 x + 3$

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Similar questions

y = ∣ ∣ x^{2} - 2 x - 3 ∣ ∣

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

(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 = x^{2} + 2 x - 3

x^{2} - x - 6 = 0

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

x^{2} - x - 6 = 0

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