a) Copy and complete the table for y = 3x^2 - 5x - 7 Table 5.16 x | -3 | -2 | -1 | 0 | 1 | 2 | 3 | 4...

Question

a) Copy and complete the table for y = 3x^2 - 5x - 7
Table 5.16
x | -3 | -2 | -1 | 0 | 1 | 2 | 3 | 4
-----------------------------------
y | 35 | | | -7 | | | 5 |
b) Using a scale of 2 cm = 1 unit along the x-axis and 2 cm = 5 units along the y-axis, draw the graph of y = 3x^2 - 5x - 7.
c) On the same axis, draw the graph of y + 3x + 2 = 0.
d) From your graph, find the:
i) the range of values of x for which x^2 - 5x - 7 < 0
ii) roots of the equation 3x^2 - 2x - 5 = 0

SnapAndSolve AI · Accepted Answer

a) Completed table for y = 3x^2 - 5x - 7

x	-3	-2	-1	0	1	2	3	4
y	35	19	5	-7	-7	5	19	35

b) Instructions for drawing the graph of y = 3x^2 - 5x - 7

Using a scale of 2 cm = 1 unit along the x-axis and 2 cm = 5 units along the y-axis, plot the points from the completed table:

(-3, 35)
(-2, 19)
(-1, 5)
(0, -7)
(1, -7)
(2, 5)
(3, 19)
(4, 35)

Connect the points to create a parabolic curve.

c) Instructions for drawing the graph of y + 3x + 2 = 0

Rewrite the equation as y = -3x - 2. Plot the points corresponding to this line:

When x = -3, y = 7
When x = -2, y = 4
When x = -1, y = 1
When x = 0, y = -2
When x = 1, y = -5

Connect these points to draw a straight line.

d) From your graph, find:

i) The range of values of x for which 3x^2 - 5x - 7 < 0:

Observe where the parabola lies below the x-axis. This occurs for:

x values in the range: (-1, 0).

ii) Roots of the equation 3x^2 - 2x - 5 = 0:

Identify x-intercepts from the graph; these will be the roots. Values are approximately:

x ≈ 2.5 and x ≈ -0.6667.

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a) Copy and complete the table for y = 3x^2 - 5x - 7 Table 5.16 x | -3 | -2 | -1 | 0 | 1 | 2 | 3 | 4...

Answer

a) Completed table for y = 3x^2 - 5x - 7

b) Instructions for drawing the graph of y = 3x^2 - 5x - 7

c) Instructions for drawing the graph of y + 3x + 2 = 0

d) From your graph, find:

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