SOLUTION: How would i show the coordinates of the vertex. And the Equation of the axis of symmetry and the greatest value of the function, for this problem? g(x)= -x2(squared)-3x

Algebra ->  Linear-equations -> SOLUTION: How would i show the coordinates of the vertex. And the Equation of the axis of symmetry and the greatest value of the function, for this problem? g(x)= -x2(squared)-3x      Log On


   

Question 140379: How would i show the coordinates of the vertex. And the Equation of the axis of symmetry and the greatest value of the function, for this problem?
g(x)= -x2(squared)-3x
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
g%28x%29=-x%5E2-3x
For any quadratic equation of the form,
f%28x%29=ax%5E2%2Bbx%2Bc
The axis of symmetry occurs at
x=-b%2F%282a%29
If a is positive, then the mininum value occurs there.
If a is negative, then the maximum value occurs there.
Comparing your equation to the standard form,
a=-1
b=-3
The axis of symmetry is
x=-b%2F%282a%29
x=-%28-3%29%2F%282%2A%28-1%29%29
x=-3%2F2
Since a is negative, the value will be a maximum.
The maximum value is,
g%28x%29=-x%5E2-3x
g%28-3%2F2%29=-%28-3%2F2%29%5E2-3%28-3%2F2%29
g%28-3%2F2%29=-%289%2F4%29%2B%289%2F2%29%29
g%28-3%2F2%29=%289%2F4%29
+graph%28+300%2C+300%2C+-5%2C+1%2C+-10%2C+10%2C+-x%5E2-3x%29+