Question

1.a) Sketch the graphs on the same axis.
(i) y = x^2 - 4
(ii) y = -x + 3

(b) What are the inequalities of the region bounded (enclosed area) by the two graphs.

Answer 1

a) $y=x^2-4$ - red line;

$y=-x+3$ - blue line.

b) $x^2-4=-x+3$

$x^2+x-7=0$

$x=\frac{-1-\sqrt{29}}{2}\;\;or\;\;x=\frac{-1+\sqrt{29}}{2}$

The region bounded by the two graphs: $\frac{-1-\sqrt{29}}{2}<x<\frac{-1+\sqrt{29}}{2}$

$x^2-4<y<-x+3$