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Cumulative Problems

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Ch. 10 Cumulative Problems

1) solve (X - 4)2 = 3

2) solve 5 (X - 2)2 = 3

3) solve - 9 (X - 3)2 = - 7

4) solve by completing the square 2 X2 - 8 X - 9 = 0

5) solve by completing the square 4 X2 + 2 X - 3 = 0

6) solve by using the quadratic formula 4 X2 - 3 X + 3 = 0

7) solve by using the quadratic formula 5 X2 - 7 X = 1

8) solve by using the quadratic formula 3 X2 = 11 X + 4

9) solve X2 + 12 X + 32 = 0

10) solve X2 + 5 X - 9 = 0

11) Graph the quadratic equation after completing the given table of values. Y = X2 - 1

X Y
- 2
- 1
0
1
2

12) Graph the quadratic equation after completing the given table of values. Y = - X2 + 1

X Y
- 2
- 1
0
1
2

13) Find the axis of symmetry. Y = X2 + X + 1

14) Find the axis of symmetry. Y = - X2 + 4 X + 2

15) Find the intercepts. Y = X2 - 5 X - 10

16) Find the intercepts. Y = X2 - 4 X + 4

17) The length of a rectangle is 3 cm more than 2 times its width. If the area of the rectangle is 99 cm2, find the dimensions of the rectangle to the nearest thousandth.

18) The height h in feet of an object after t seconds is given by the function
h = - 16 t 2 + 60 t + 9
How long will it take the object to hit the ground? Round your answer to the nearest thousandth.

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Solution Summary

Cumulative problems are solved for equations.

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Ch. 10 Cumulative Problems

1) solve (X - 4)2 = 3
Solution:

Take square root on each side, we will get
X - 4 = ±√3

Add 4 to each side, we will get

X = 4± √3

Solutions are X = 4 - √3, 4 + √3

2) solve 5 (X - 2)2 = 3

Divide each side by 5, we will get

(X - 2)2 = 3/5

Take square root on each side, we will get
X - 2 = ±√(3/5)

X = 2±√(3/5)

The solutions are

Or in decimals X = 1.225, 2.775

3) solve - 9 (X - 3)2 = - 7

Divide each side by -9, we will get
(X - 3)2 = 7/9
Take square root

The solutions are
Or in decimals X = 2.118, 3.882

4) solve by completing the square 2 X2 - 8 X - 9 = 0

Solution:
We can write it as
2 X2 - 8 X = 9

Divide each side by 2
X2 - 4 X = 9/2

Add 4 to each side
X2 - 4 X + 4 = 9/2 + 4

(X - 2) 2= 17/2

Take square root, we will get

The solutions are
Or in decimals X = -0.915, 4.915

5) solve by completing the square 4 X2 + 2 X - 3 = 0

we can write it as

4 X2 + 2 X = 3

Add 1/4 on each side

4 X2 + 2 X + 1/4 = 3 + ¼
(2X + ½)^2 = 13/4

Take square ...

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  • MSc, Meerut University
  • MPhil, Institute of Advanced Studies
  • MSc, AIT
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