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

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Solution

As we know the graph for $y = x^{2} - 2 x - 3 = (x - 3) (x + 1)$ is a parabola;
So to sketch $y = ∣ ∣ x^{2} - 2 x - 3 ∣ ∣$ we have to follow two steps:
$(i)$ Leave the positive part of $y = x^{2} - 2 x - 3$ , as it is
$(i i)$ Take the image of negative part of $y = x^{2} - 2 x - 3$ ,
i.e., the part below $x -$ axis in the $x -$ axis as plane mirror shown below.
Graph for $y = x^{2} - 2 x - 3 = (x - 3) (x + 1)$ is plotted as
x -2 -1 0 1 2 -3 3 $- \infty$ $\infty$
y 5 0 -3 -4 -3 12 0 $\infty$ $\infty$

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Similar questions

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

y = x^{2} + 2 x + 1

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

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