SOLUTION: Find the equation, in vertex form, of the quadratic equation with zeros -1 and 7 and through the point (5,6). Include a sketch.

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 = a(x+1)(x-7)  |Using P(5,6), 6 = a(-12) , a = (-1/2)

 y =-1/2(x^2 - 6x - 7)  0r by taking the -7 outside the parenthesis

 y = -1/2(x^2-6x) +7/2  Completing the Square

  y = -1/2(x^2-6x +9  -9) +7/2    |taking the -9 outside the parenthesis

 y = -1/2(x-3)^2 +9/2 + 7/2 0r

 y = -1/2(x-3)^2  + 8     V(3,8) & crosses x-axis at x = -1  and x=7

Wish You the Best in your Studies.