Question 812761
The y-intercept is the point where the graph crosses the y-axis,
which is the line {{{x=0}}} ,
or the y-coordinate of that point, since we know that the point has {{{x=0}}} .
We know it is only one point, because a function has at most one value of {{{y=f(x)}}} for each value of {{{x}}},
so for {{{x=0}}}, there is just one value of {{{y=f(x)}}} .
In other words, the graph of a function cannot cross a vertical line (like {{{x=0}}} ) more than once.
{{{system(x=0,y=-0.20(x-7)^2+15)}}} --> {{{y=-0.20(0-7)^2+15)}}} --> {{{y=-0.20*(-7)^2+15)}}} --> {{{y=-0.20*49+15)}}} --> {{{y=-9.8+15)}}} --> {{{highlight(y=5.2))}}}
You would know if the answer is expected to be given as
{{{highlight(y=5.2))}}} or as {{{highlight( "( 0 , 5.2 )" )}}} .
 
The x-intercept is the point (or points) where the graph crosses the x-axis,
which is the line {{{y=0}}} ,
or the x-coordinate of that point, since we know that the point has {{{y=0}}} .
{{{system(y=0,y=-0.20(x-7)^2+15)}}} --> {{{0=-0.20(x-7)^2+15)}}}-->{{{0.20(x-7)^2=15)}}}-->{{{(x-7)^2=15/0.20}}}-->{{{(x-7)^2=75}}}-->{{{system(x-7=sqrt(75),"or",x-7=-sqrt(75))}}} -->{{{highlight(x=7 +- sqrt(75))}}} or {{{highlight(x=7 +- 5sqrt(3))}}} .
The approximate values, are {{{x=-1.66}}} and {{{x=15.66}}}
Again, you would know how you are expected to format the answer.