Worksheet: Completing Square 1. What value of b makes the ...
Worksheet: Completing Square 1. What value of b makes the ...
Worksheet: Completing Square 1. What value of b makes the ...
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<strong>Worksheet</strong>: <strong>Completing</strong> <strong>Square</strong><br />
<strong>1.</strong> <strong>What</strong> <strong>value</strong> <strong>of</strong> b <strong>makes</strong> <strong>the</strong> expression x 2 + bx + 4 a perfect square?<br />
a) 0<br />
b) 1<br />
c) 2<br />
d) 4<br />
2. <strong>What</strong> <strong>value</strong> <strong>of</strong> b <strong>makes</strong> <strong>the</strong> expression x 2 + bx + 169 a perfect square?<br />
a) 0<br />
b) 13<br />
c) 26<br />
d) 169<br />
3. <strong>What</strong> <strong>value</strong> <strong>of</strong> c <strong>makes</strong> <strong>the</strong> expression x 2 + 6x + c a perfect square?<br />
a) 0<br />
b) 9<br />
c) 36<br />
d) 144<br />
4. <strong>What</strong> <strong>value</strong> <strong>of</strong> c <strong>makes</strong> <strong>the</strong> expression x 2 – 22x + c a perfect square?<br />
a) 121<br />
b) –484<br />
c) 484<br />
d) 1936<br />
2<br />
5. <strong>What</strong> is <strong>the</strong> maximum <strong>value</strong> <strong>of</strong> y in <strong>the</strong> relation y = – 3 (x – 5) 2 + 11?<br />
a) –11<br />
b) –5<br />
c) 5<br />
d) 11<br />
6. <strong>What</strong> is <strong>the</strong> minimum <strong>value</strong> <strong>of</strong> y in <strong>the</strong> relation y = 7(x – 6) 2 – 19?<br />
a) –19<br />
b) –16<br />
c) 16<br />
d) 19
7. <strong>What</strong> <strong>value</strong> must be added to <strong>the</strong> expression x 2 + 12x to make it a perfect square?<br />
a) 6<br />
b) 12<br />
c) 36<br />
d) 144<br />
8. <strong>What</strong> <strong>value</strong> must be added to <strong>the</strong> expression x 2 – 10x to make it a perfect square?<br />
a) –25<br />
b) –5<br />
c) 5<br />
d) 25<br />
9. <strong>What</strong> <strong>value</strong> must be added to <strong>the</strong> expression x 2 + 22x + 97 to make it a perfect square?<br />
a) 22<br />
b) 24<br />
c) 97<br />
d) 121<br />
10. <strong>What</strong> <strong>value</strong> <strong>of</strong> k <strong>makes</strong> x 2 – 28x – 100 = (x – 14) 2 + k true?<br />
a) k = –296<br />
b) k = – 196<br />
c) k = –96<br />
d) k = 96<br />
1<strong>1.</strong> <strong>What</strong> <strong>value</strong>s <strong>of</strong> b make <strong>the</strong> expression x 2 + bx + 100 a perfect square?<br />
12. <strong>What</strong> <strong>value</strong>s <strong>of</strong> b make <strong>the</strong> expression x 2 + bx + <strong>1.</strong>44 a perfect square?<br />
13. <strong>What</strong> <strong>value</strong>s <strong>of</strong> c make <strong>the</strong> expression x 2 – 32x + c a perfect square?<br />
14. Write y = 3x 2 + 12x in vertex form.
15. Write y = –7x 2 + 42x – 3 in vertex form.<br />
16. Write y = 0.6x 2 – 9x + 3.5 in vertex form.<br />
17. A ball is kicked from <strong>the</strong> ground into <strong>the</strong> air. The height <strong>of</strong> <strong>the</strong> ball, h, in metres,<br />
after t seconds is modelled by h = 30t – 5t 2 . How long is <strong>the</strong> ball in <strong>the</strong> air?<br />
18. A ball is kicked from <strong>the</strong> ground into <strong>the</strong> air. The height <strong>of</strong> <strong>the</strong> ball h, in metres, after<br />
t seconds is modelled by h = 30t – 5t 2 . Find <strong>the</strong> greatest height <strong>the</strong> ball reaches.<br />
19. Describe a method to find <strong>the</strong> coordinates <strong>of</strong> <strong>the</strong> vertex <strong>of</strong> y = 5(x – 4)(x + 7).<br />
20. List <strong>the</strong> transformations applied to <strong>the</strong> graph <strong>of</strong> y = x 2 to produce a graph that can be<br />
modelled by y = –3x 2 + 24x + 17?
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