Question 243661
{{{y=-x^2+16x}}}
<pre><font size = 4 color = "indigo"><b>
Start with this t-table:

 x | y
-------
   | 0
   |
   |

First find the x-intercepts by substituting 0 for y

{{{0=-x^2+16x}}}

{{{x^2-16x=0}}}

{{{x(x-16)=0}}}

{{{x=0}}}

{{{x-16=0}}}
{{{x=16}}}

This give us two points with y=0

 x | y
-------
 0 | 0
16 | 0
   |

Now choose a value of x halfway between
the two x-intercepts:

 x | y
-------
 0 | 0
16 | 0
 8 |

{{{y=-x^2+16x}}}
{{{y=-(8)^2+16(8)}}}
{{{y=-64+128}}}
{{{y=64}}}

So we have this t-table:

 x |  y
--------
 0 |  0
16 |  0
 8 | 64

Use a large scale to accommodate those points.
It is not necessary to mark off the x-axis and 
y-axis with the same scale.

Plot those three points:

{{{drawing(400,400,-10,20,-30,100,
graph(400,400,-10,20,-30,100),
locate(0,7,"(0,0)"), locate(8,71,"(8,64)"), locate(16,7,"(16,0)"),
line(0+.3,0,0-.3,0), line(0+.3,0,0-.3,0), line(0+.3,0+.3,0-.3,0-.3), line(0+.3,0-.3,0-.3,0+.3), 

line(16+.3,0,16-.3,0), line(16,0+.3,16,0-.3), line(16+.3,0+.3,16-.3,0-.3), line(16+.3,0-.3,16-.3,0+.3),

line(8+.3,64,8-.3,64), line(8,64+.3,8,64-.3), line(8+.3,64+.3,8-.3,64-.3), line(8+.3,64-.3,8-.3,64+.3)
 )}}}

Draw an upside-down U-shaped curve through those two points:

{{{drawing(400,400,-10,20,-30,100,
graph(400,400,-10,20,-30,100,-x^2+16x),
locate(0,7,"(0,0)"), locate(8,71,"(8,64)"), locate(16,7,"(16,0)"),
line(0+.3,0,0-.3,0), line(0+.3,0,0-.3,0), line(0+.3,0+.3,0-.3,0-.3), line(0+.3,0-.3,0-.3,0+.3), 

line(16+.3,0,16-.3,0), line(16,0+.3,16,0-.3), line(16+.3,0+.3,16-.3,0-.3), line(16+.3,0-.3,16-.3,0+.3),

line(8+.3,64,8-.3,64), line(8,64+.3,8,64-.3), line(8+.3,64+.3,8-.3,64-.3), line(8+.3,64-.3,8-.3,64+.3)
 )}}}

Edwin</pre>