5.1 Homework due Tue 29.9.15

To be done neatly in the front of your books
TOTAL 22 marks

1. The plots shows the curve $y=x^2+4x-1$

   

   1. Use the formula to solve the equation $x^2+4x-1=0$ giving your answers to 2 d.p.
   2. $x^2+4x-1=k$ has no solutions, where k is an integer. Use the plot above to find the maximum value of k

   [4 marks]

2. Complete the square $x^2+8x-4$ and use your answer to solve $x^2+8x-4=0$, leaving your answers in surd form

   [3 marks]

3. Y varies indirectly as the square root of x. If y=7 when x=4, then:
   1. Find a formula for y in terms of x
   2. Find y when x=10 to 3 s.f.
   3. Find x when y=2.2

   [4 marks]

4. Find the image of the point (-2, -3) under the transformation represented by M $M = \begin{pmatrix} 4 & -3 \\ -5 & -7 \end{pmatrix}$

   [2 marks]

5. Find the 2x2 matrix which represents a reflection in the x axis.

   [2 marks]

6. Write $2x^2+6x -3$ in the form $a(x+b)^2 +c$.

   [3 marks]

7. Draw up a table of values for $-2 \leq x \leq 3$ for the function $y=x^3 -2x^2+x-3$ and use it to sketch the curve neatly (and with appropriate scales).

   [4 marks]