Question

write the equation in vertex form for the quadratic function with vertex (-6,4) and passing through point (-2,12).show your work

Answer 1

y =
`(1)/(2)`(x + 6)² + 4

the equation of a quadratic 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 ) = (- 6, 4 ), hence

y = a(x + 6 )² + 4

To find a substitute (- 2, 12) into the equation

12 = 16a + 4 ( subtract 4 from both sides )

8 = 16a ( divide both sides by 16 )

a =
`(8)/(16)` =
`(1)/(2)`

y =
`(1)/(2)`(x + 6 )² + 4 ← in vertex form