2.3 Übungen
Aus Online Mathematik Brückenkurs 1
(Unterschied zwischen Versionen)
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| - | === | + | ===Übung 2.3:1=== |
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Complete the square of the expressions | Complete the square of the expressions | ||
| Zeile 22: | Zeile 22: | ||
</div>{{#NAVCONTENT:Answer|Answer 2.3:1|Solution a|Solution 2.3:1a|Solution b|Solution 2.3:1b|Solution c|Solution 2.3:1c|Solution d|Solution 2.3:1d}} | </div>{{#NAVCONTENT:Answer|Answer 2.3:1|Solution a|Solution 2.3:1a|Solution b|Solution 2.3:1b|Solution c|Solution 2.3:1c|Solution d|Solution 2.3:1d}} | ||
| - | === | + | ===Übung 2.3:2=== |
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Solve the following second order equations by completing the square | Solve the following second order equations by completing the square | ||
| Zeile 42: | Zeile 42: | ||
</div>{{#NAVCONTENT:Answer|Answer 2.3:2|Solution a|Solution 2.3:2a|Solution b|Solution 2.3:2b|Solution c|Solution 2.3:2c|Solution d|Solution 2.3:2d|Solution e|Solution 2.3:2e|Solution f|Solution 2.3:2f}} | </div>{{#NAVCONTENT:Answer|Answer 2.3:2|Solution a|Solution 2.3:2a|Solution b|Solution 2.3:2b|Solution c|Solution 2.3:2c|Solution d|Solution 2.3:2d|Solution e|Solution 2.3:2e|Solution f|Solution 2.3:2f}} | ||
| - | === | + | ===Übung 2.3:3=== |
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Solve the following equations directly | Solve the following equations directly | ||
| Zeile 63: | Zeile 63: | ||
</div>{{#NAVCONTENT:Answer|Answer 2.3:3|Solution a|Solution 2.3:3a|Solution b|Solution 2.3:3b|Solution c|Solution 2.3:3c|Solution d|Solution 2.3:3d|Solution e|Solution 2.3:3e|Solution f|Solution 2.3:3f}} | </div>{{#NAVCONTENT:Answer|Answer 2.3:3|Solution a|Solution 2.3:3a|Solution b|Solution 2.3:3b|Solution c|Solution 2.3:3c|Solution d|Solution 2.3:3d|Solution e|Solution 2.3:3e|Solution f|Solution 2.3:3f}} | ||
| - | === | + | ===Übung 2.3:4=== |
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Determine a second-degree equation which has roots | Determine a second-degree equation which has roots | ||
| Zeile 78: | Zeile 78: | ||
</div>{{#NAVCONTENT:Answer|Answer 2.3:4|Solution a|Solution 2.3:4a|Solution b|Solution 2.3:4b|Solution c|Solution 2.3:4c}} | </div>{{#NAVCONTENT:Answer|Answer 2.3:4|Solution a|Solution 2.3:4a|Solution b|Solution 2.3:4b|Solution c|Solution 2.3:4c}} | ||
| - | === | + | ===Übung 2.3:5=== |
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{| width="100%" cellspacing="10px" | {| width="100%" cellspacing="10px" | ||
| Zeile 92: | Zeile 92: | ||
</div>{{#NAVCONTENT:Answer|Answer 2.3:5|Solution a|Solution 2.3:5a|Solution b|Solution 2.3:5b|Solution c|Solution 2.3:5c}} | </div>{{#NAVCONTENT:Answer|Answer 2.3:5|Solution a|Solution 2.3:5a|Solution b|Solution 2.3:5b|Solution c|Solution 2.3:5c}} | ||
| - | === | + | ===Übung 2.3:6=== |
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Determine the smallest value that the following polynomial can take | Determine the smallest value that the following polynomial can take | ||
| Zeile 106: | Zeile 106: | ||
| - | === | + | ===Übung 2.3:7=== |
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Determine the largest value that the following polynomials can take. | Determine the largest value that the following polynomials can take. | ||
| Zeile 119: | Zeile 119: | ||
</div>{{#NAVCONTENT:Answer|Answer 2.3:7|Solution a|Solution 2.3:7a|Solution b|Solution 2.3:7b|Solution c|Solution 2.3:7c}} | </div>{{#NAVCONTENT:Answer|Answer 2.3:7|Solution a|Solution 2.3:7a|Solution b|Solution 2.3:7b|Solution c|Solution 2.3:7c}} | ||
| - | === | + | ===Übung 2.3:8=== |
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Sketch the graph of the following functions | Sketch the graph of the following functions | ||
| Zeile 132: | Zeile 132: | ||
</div>{{#NAVCONTENT:Answer|Answer 2.3:8|Solution a|Solution 2.3:8a|Solution b|Solution 2.3:8b|Solution c|Solution 2.3:8c}} | </div>{{#NAVCONTENT:Answer|Answer 2.3:8|Solution a|Solution 2.3:8a|Solution b|Solution 2.3:8b|Solution c|Solution 2.3:8c}} | ||
| - | === | + | ===Übung 2.3:9=== |
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Find all the points where the x-axis and the following curves intersect. | Find all the points where the x-axis and the following curves intersect. | ||
| Zeile 145: | Zeile 145: | ||
</div>{{#NAVCONTENT:Answer|Answer 2.3:9|Solution a|Solution 2.3:9a|Solution b|Solution 2.3:9b|Solution c|Solution 2.3:9c}} | </div>{{#NAVCONTENT:Answer|Answer 2.3:9|Solution a|Solution 2.3:9a|Solution b|Solution 2.3:9b|Solution c|Solution 2.3:9c}} | ||
| - | === | + | ===Übung 2.3:10=== |
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In the ''xy''-plane, draw in all the points whose coordinates <math>\,(x,y)\,</math> satisfy | In the ''xy''-plane, draw in all the points whose coordinates <math>\,(x,y)\,</math> satisfy | ||
Version vom 09:14, 22. Okt. 2008
Übung 2.3:1
Complete the square of the expressions
| a) | \displaystyle x^2-2x | b) | \displaystyle x^2+2x-1 | c) | \displaystyle 5+2x-x^2 | d) | \displaystyle x^2+5x+3 |
Answer
Laden...
Solution a
Solution b
Solution c
Solution d
Übung 2.3:2
Solve the following second order equations by completing the square
| a) | \displaystyle x^2-4x+3=0 | b) | \displaystyle y^2+2y-15=0 | c) | \displaystyle y^2+3y+4=0 |
| d) | \displaystyle 4x^2-28x+13=0 | e) | \displaystyle 5x^2+2x-3=0 | f) | \displaystyle 3x^2-10x+8=0 |
Answer
Solution a
Solution b
Solution c
Solution d
Solution e
Solution f
Übung 2.3:3
Solve the following equations directly
| a) | \displaystyle x(x+3)=0 | b) | \displaystyle (x-3)(x+5)=0 |
| c) | \displaystyle 5(3x-2)(x+8)=0 | d) | \displaystyle x(x+3)-x(2x-9)=0 |
| e) | \displaystyle (x+3)(x-1)-(x+3)(2x-9)=0 | f) | \displaystyle x(x^2-2x)+x(2-x)=0 |
Answer
Solution a
Solution b
Solution c
Solution d
Solution e
Solution f
Übung 2.3:4
Determine a second-degree equation which has roots
| a) | \displaystyle -1\ and \displaystyle \ 2 |
| b) | \displaystyle 1+\sqrt{3}\ and \displaystyle \ 1-\sqrt{3} |
| c) | \displaystyle 3\ and \displaystyle \ \sqrt{3} |
Answer
Solution a
Solution b
Solution c
Übung 2.3:5
| a) | Determine a second-degree equation which only has \displaystyle \,-7\, as a root. |
| b) | Determine a value of \displaystyle \,x\, which makes the expression \displaystyle \,4x^2-28x+48\, negative. |
| c) | The equation \displaystyle \,x^2+4x+b=0\, has one root at \displaystyle \,x=1\,. Determine the value of the constant \displaystyle \,b\,. |
Answer
Solution a
Solution b
Solution c
Übung 2.3:6
Determine the smallest value that the following polynomial can take
| a) | \displaystyle x^2-2x+1 | b) | \displaystyle x^2-4x+2 | c) | \displaystyle x^2-5x+7 |
Answer
Solution a
Solution b
Solution c
Übung 2.3:7
Determine the largest value that the following polynomials can take.
| a) | \displaystyle 1-x^2 | b) | \displaystyle -x^2+3x-4 | c) | \displaystyle x^2+x+1 |
Answer
Solution a
Solution b
Solution c
Übung 2.3:8
Sketch the graph of the following functions
| a) | \displaystyle f(x)=x^2+1 | b) | \displaystyle f(x)=(x-1)^2+2 | c) | \displaystyle f(x)=x^2-6x+11 |
Answer
Solution a
Solution b
Solution c
Übung 2.3:9
Find all the points where the x-axis and the following curves intersect.
| a) | \displaystyle y=x^2-1 | b) | \displaystyle y=x^2-5x+6 | c) | \displaystyle y=3x^2-12x+9 |
Answer
Solution a
Solution b
Solution c
Übung 2.3:10
In the xy-plane, draw in all the points whose coordinates \displaystyle \,(x,y)\, satisfy
| a) | \displaystyle y \geq x^2\ and \displaystyle \ y \leq 1 | b) | \displaystyle y \leq 1-x^2\ and \displaystyle \ x \geq 2y-3 |
| c) | \displaystyle 1 \geq x \geq y^2 | d) | \displaystyle x^2 \leq y \leq x |
Answer
Solution a
Solution b
Solution c
Solution d
