tmua 2022 Q12

tmua · Uk · paper1 1 marks Completing the square and sketching Two quadratic functions: intersection, tangency, or equality conditions

A family of quadratic curves is given by
$$y _ { k } = 2 \left( x - \frac { k } { 2 } \right) ^ { 2 } + \frac { k ^ { 2 } } { 2 } + 4 k + 3$$
where $k$ is any real number and $y _ { k }$ is a function of $x$.
All these curves are sketched, and the point with the lowest $y$-coordinate among all the curves $y _ { k }$ is $( a , b )$.
Find the value of $a + b$

..... 14

A family of quadratic curves is given by

$$y _ { k } = 2 \left( x - \frac { k } { 2 } \right) ^ { 2 } + \frac { k ^ { 2 } } { 2 } + 4 k + 3$$

where $k$ is any real number and $y _ { k }$ is a function of $x$.

All these curves are sketched, and the point with the lowest $y$-coordinate among all the curves $y _ { k }$ is $( a , b )$.

Find the value of $a + b$

Paper Questions

Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 Q16 Q17 Q18 Q19 Q20