SOLUTION: Determine the following for each quadratic function shown below: the direction of opening, the coordinates of the vertex, the equation of the axis of symmetry, and the maximum/min

Algebra ->  Graphs -> SOLUTION: Determine the following for each quadratic function shown below: the direction of opening, the coordinates of the vertex, the equation of the axis of symmetry, and the maximum/min      Log On


   

Question 1173304: Determine the following for each quadratic function shown below: the direction of opening, the coordinates of the vertex, the equation of the axis of symmetry, and the maximum/minimum value and when it occurs.
y=-x2+10x+7
y=-3x2+12x-17
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi  

Note: the vertex form of a Parabola opening up(a>0) or down(a<0), 

y=a%28x-h%29%5E2+%2Bk 

where(h,k) is the vertex  and  x = h  is the Line of Symmetry.

 y= -x^2+10x+7   0r

  y= -(x^2-10x) + 7  

Completing the Square  

 y= -(x^2-10x +25  -25)+ 7  0r by taking the -25 outside the parenthesis

 y = -(x^2-5)   + 25 +7 

  y = -(x^2-5) + 32    

 V(5,32)  and line of Symmetry is x = 5

Maximum at P(5,32)

Wish You the Best in your Studies.  



As to: y=-3x^2+12x-17 Completing the Square: Same Steps as Above 

y = -3(x-2)^2 -5  V(2,-5)max  and Line of Symmetry is x = 2