Question

Draw the graphs of (i) y = x2 – x – 6 (ii) y = 6 – x – x2 and find zeros in each case. What do you notice?

Answer 1

Dear Student,

graph of 1: (i) y = x2 – x – 6 is shown in green color in attachment image.


graph of 1: (i) y = 6 – x – x2 is shown in orange
color in attachment image.

zeros of both equations:
1) x2 – x – 6

${x }^{2} - x - 6 = 0 \\ \\ {x}^{2} - 3x + 2x - 6 = 0 \\ \\ x(x - 3) + 2(x - 3) = 0 \\ \\ (x - 3)(x + 2) = 0 \\ x - = 0 \\ x = 3 \\ (x + 2) = 0 \\ x = - 2$

2)
$6 - x - {x}^{2} = 0 \\ \\ - {x}^{2} - x + 6 = 0 \: \: \: \: or \\ {x}^{2} + x - 6 = 0 \\ \\ {x}^{2} + 3x - 2x - 6 = 0 \\ \\x (x + 3) - 2(x + 3) = 0 \\ \\ (x + 3)(x - 2) = 0 \\ \\ x + 3 = 0 \\ \\ x = - 3 \\ \\ x - 2 = 0 \\ \\ x = 2$
hope the solution helps you.

Answer 2

Step-by-step explanation:

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