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Complete the table given below for the equation y = 5 + 3x − 2x² by filling in the blank spaces. Use the values from the table above to draw the graph of y = 5 + 3x − 2x². Use your graph to determine the ranges of values of x which satisfy the inequality 5 + 3x - 2x² ≤ -2.

July 30, 2026Mathematics

ScanSolve AI Answer

Answer

5

Graph of y = 5 + 3x − 2x²

Key points of y = 5 + 3x − 2x²
Point	x	y
x-intercept	−1	0
y-intercept	0	5
Maximum	0.75	6.13
x-intercept	2.5	0

Step-by-step solution

2 steps

Ili kukamilisha jedwali, tutatumia mlinganyo $y = 5 + 3x - 2x^2$ kuhesabu thamani ya $y$ kwa kila thamani ya $x$ . Thamani pekee inayokosekana ni kwa $x = 1.5$ .

Badilisha $x = 1.5$ kwenye mlinganyo.
$y = 5 + 3(1.5) - 2(1.5)^2$
Rahisisha mlinganyo.
$y = 5 + 4.5 - 2(2.25)$ $y = 5 + 4.5 - 4.5$ $y = 5$
Jedwali lililokamilika ni kama ifuatavyo:

x -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5
y -9 -4 0 3 5 6 6 5 3 0 -4 -9

Thamani inayokosekana ni $*5*$ .