Question

The graph of a quadratic function goes through a vertex of (105, 27) and also (109, 14),

What is the value of “a” for this function?

Answer 1

a = -
`(13)/(16)`

Explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Here (h, k ) = (105, 27 ) , thus

y = a(x - 105)² + 27

To find a substitute (109, 14 ) into the equation

14 = a(109 - 105)² + 27 ( subtract 27 from both sides )

- 13 = 16a ( divide both sides by 16 )

a = -
`(13)/(16)`