Question

Find the equation that passing through the point (4,6) and has a vertex of (2,-3)

Answer 1

y =
`(9)/(4)` (x - 2)² - 3

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 ) = (2, - 3 ) , then

y = a(x - 2)² - 3

To find a substitute (4, 6 ) into the equation

6 = a(4 - 2)² - 3 ( add 3 to both sides )

9 = a(2)² = 4a ( divide both sides by 4 )

`(9)/(4)` = a

y =
`(9)/(4)` (x - 2)² - 3 ← in vertex form