examday

/TMUA

A curve $C$ has equation $y=px^2+qx+r$, where $p\ne0$. The curve $C$ is reflected in the $x$-axis to give a curve $C'$. The curve $C$ is then translated 3 units to the right to give the graph of $y=f(x)$, and $C'$ is translated 3 units to the left to give the graph of $y=g(x)$.

Consider the following four statements about the graph of $y=(f+g)(x)$.

• I The graph of $y=(f+g)(x)$ is a straight line.
• II The $y$-intercept of the line equals $-r$.
• III The gradient of the line is determined solely by $p$; it does not depend on $q$ or $r$.
• IV If $p>0$ and $q>0$, the line has negative gradient and negative $y$-intercept.