Question

Solve :
(a) (i) Complete the table of values for $y=-x^2+5x$.

$x$	$-1$	$0$	$1$	$2$	$3$	$4$	$5$	$6$
$y$	$-6$		$4$			$4$	$0$

(ii) On the grid, draw the graph of $y=-x^2+5x$ for $-1<x<6$.
(b) Write down the co-ordinates of the highest point on the graph.
(c) Use your graph to solve the equation $-x^2+5x=-3$.
(d) (i) On the grid draw, the line of symmetry for the graph.
(ii) Write down the equation of the line of symmetry for the graph.

Answer 1

Given $y=-x^2+5x$

1) When $x=0$,

$y=-{\left(0\right)}^2+5\left(0\right)$

$\therefore y=0$

2) When $x=2$,

$y=-{\left(2\right)}^2+5\left(2\right)$

$\therefore y=-4+10$

$\therefore y=6$

3) When $x=3$,

$y=-{\left(3\right)}^2+5\left(3\right)$

$\therefore y=-9+15$

$\therefore y=6$

4) When $x=6$,

$y=-{\left(6\right)}^2+5\left(6\right)$

$\therefore y=-36+30$

$\therefore y=-6$

5) Co-ordiantes of highest point on graph are $(3,6)$

6) Given $-x^2+5x=-3$

Compare this equation with given equation $-x^2+5x=y$, we get,

$y=-3$

From the figure, it is clear that,

when $y=-3$, $x\approx 5.6$