2.3 Exercises
From Förberedande kurs i matematik 1
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===Exercise 2.3:10=== | ===Exercise 2.3:10=== | ||
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| - | In the ''xy''-plane, | + | In the ''xy''-plane, shade in the area whose coordinates <math>\,(x,y)\,</math> satisfy |
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Current revision
| Theory | Exercises |
Exercise 2.3:1
Complete the square of the expressions
| a) | | b) | | c) | | d) | |
Answer | Solution a | Solution b | Solution c | Solution d
Loading...Exercise 2.3:2
Solve the following second order equations by completing the square
| a) | | b) | | c) | |
| d) | | e) | | f) | |
Answer | Solution a | Solution b | Solution c | Solution d | Solution e | Solution f
Exercise 2.3:3
Solve the following equations directly
| a) | | b) | |
| c) | | d) | |
| e) | | f) | |
Answer | Solution a | Solution b | Solution c | Solution d | Solution e | Solution f
Exercise 2.3:4
Find 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
Exercise 2.3:5
| a) | Find 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
Exercise 2.3:6
Determine the smallest value that the following polynomials 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
Exercise 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
Exercise 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
Exercise 2.3:9
Find all the points where the following curves intersect the \displaystyle x-axis.
| 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
Exercise 2.3:10
In the xy-plane, shade in the area 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
