Finding coefficient of the squared expression in the equation

Question

if the vertex of a parabola is (5,5) and the x-value is 6 and the y-value is -1 what is the coefficient of the squared expression in the parabolas equation 

Answer 1

First, you need the formula for the vertex equation:  y = a*(x - h)² + k , where (h,k) is the vertex.

 

Second, use the vertex given and you should end up with y = a*(x - 5)² + 5.

 

y = a*[(x - 5)(x - 5) + 5] by using squared binomials

y = a*[(x² - 10x + 25) + 5] by FOIL

y = a*(x² -10x + 30) by combining like terms

 

Once you have the equation above, plug in the given point (6, -1) to find a.

 

-1 = a*[6² - 10(6) + 30]

-1 = a*(36 - 60 + 30)

-1 = 6a

 

Therefore, a = -1/6.

 

Hope this helps.