Question

Question 5: Graph the inequality. y> 3x² + 3x - 5 Question 6: Determine graphically, the solution region for the two inequalities. y > 22 - 3x - 6 and y> 2x2 + 7x + 6 Question 7: Solve the inequality algebraically and show the solution in interval form. x² + 2x - 3 > 0 Question 8: Solve the inequality algebraically and show the solution in interval form. 2x2 - 6x - 9> 11

Answer 1

Answer 5:

Given inequality :  

y > 3.12 + 3.1 – 5

Now, we can rewrite the given inequality as -

y > 3.12 + 3.1 – 5

y > 3(.+) - 5

1- y> 3.x + C+ 1-4 4

J> 3(r + - ) – 3

+)£< C

- + x){ <fi

As we can see that the above equation represents an upward parabola (a = 3 > 0 ) with the vertex .

NA

We can find the x-intercepts as -

+ 2)£ = 0

=3(T+ 1-2

=(x+3)

+ =- 41.34

: x= 1.3844 – 0.5 and r= -1.3844 – 0.5

:. I = 0.8844 and I = -1.8844

Similarly, we can find the y-intercepts as -

y = 3(0+ 2

$y = 3(\frac{1}{4}) -\frac{23}{4}$

$y = \frac{3}{4} -\frac{23}{4}$

$y = -\frac{20}{4}$

y = -5

Using the above data, we can plot the graph for the inequality as -

ܣ ܙ !_ ܚܚܝ (-l.884, 0) (0.884, 0) -8 f - 6 5 -4 -3 -2 . 0 234567 ܝ ܀ ܚ ܀ ܘ (0, -5) ܀ (-0.5, -5.75) ܙܪ ܞ