The diagram shows the graph of $y=x^2+ax+4$ and $y=x^2+bx+c$. The graph of $y=x^2+ax+4$ touche

Question

The diagram shows the graph of $y=x^2+ax+4$ and $y=x^2+bx+c$. The graph of $y=x^2+ax+4$ touches the $x$-axis at $P$. Points $M$ and $O$ are the $x$-intercepts of the graph of $y=x^2+bx+c$. The origin $O$ is the mid-point of $MP$. Find the values of $a$, $b$ and $c$.[4] The graph of $y=x^2+ax+4$ and $y=x^2+bx+c$ intersects at $N$. Find the coordinates of $N$.[2] The graph $y=px^2+qx+r$ has its turning point at $N$ and passes through point $P$. Find the values of $p$, $q$ and $r$, where $r>0$.[3]

Accepted Answer

(a) $a=-4$, $b=2$, $c=0$ (b) $N=\left(\frac{2}{3},\frac{16}{9}\right)$ (c) $p=-1$, $q=\frac{4}{3}$, $r=\frac{4}{3}$

2025 AISS PRELIMS P2 Q6

2025 AISS PRELIMS P2 Q6

Solution:

Solution locked