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 ...
Education
- BSc, Meerut University
- MSc, Meerut University
- MPhil, Institute of Advanced Studies
- MSc, AIT
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