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

Hi  

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

 

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

y=2x^2+12x+65  0r Completing the Square

y= 2(x^2+6x +9) -18 + 65  

y= 2(x+3)^2) + 47

V(-3,47)  and x = -3 is the Line of Symmetry

Minimum Value is at  P(-3,47) 



y=-7x^2+14x+3 0r Completing the Square

y = -7(x^2 - 2x +1)+7 +3

y =(x-1)^2-4  C(1, 10)  and x = 1 is the Line of Symmetry

Maximum Value is at  P(1, 10)

Wish You the Best in your Studies.