SOLUTION: The height, y, of a ball tossed into the air can be represented by the equation {{{ y= -x^2+10x+3 }}} , where x is the elapsed time. What is the equation of the axis of symmetry of

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: The height, y, of a ball tossed into the air can be represented by the equation {{{ y= -x^2+10x+3 }}} , where x is the elapsed time. What is the equation of the axis of symmetry of      Log On


   

Question 715744: The height, y, of a ball tossed into the air can be represented by the equation +y=+-x%5E2%2B10x%2B3+ , where x is the elapsed time. What is the equation of the axis of symmetry of this parabola?
Found 2 solutions by KMST, lwsshak3:
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
It's highlight%28x=5%29 .
If a parabola has the equation y=ax%5E2%2Bbx%2Bc
the equation of its axis of symmetry is x=-b%2F2a
In your case a=-1 and b=10, so -b%2F2a=-10%2F2%2F%28-1%29=5

However, you do not need to remember formulas if you realize that you can transform the equation +y=+-x%5E2%2B10x%2B3+ into
y=-%28x-5%29%5E2%2Bsomething
-%28x-5%29%5E2=-%28x%5E2-10x%2B25%29=-x%5E2%2B10x-25 so adding 28 to both sides of
-%28x-5%29%5E2=-x%5E2%2B10x-25 we get
-%28x-5%29%5E2%2B28=-x%5E2%2B10x%2B3
which tells you that y=-%28x-5%29%5E2%2B28 is another form of the equation of your parabola,
and this form tells you that the maximum height is 28, reached at time 5.

Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
The height, y, of a ball tossed into the air can be represented by the equation +y=+-x%5E2%2B10x%2B3+ , where x is the elapsed time. What is the equation of the axis of symmetry of this parabola?
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Vertex form of equation for a parabola that opens upward: y=A(x-h)^2+k, (h,k)=(x,y) coordinates of the vertex
complete the square
y= -(x^2-10x+25)+25+3
y=-(x-5)^2+28
vertex(5,28)
axis of symmetry: x=5