Question

Write the equation of the parabola that has the vertex at point (1,3) and passes through the point (−1,5).

y=

Answer 1

y =
`(1)/(2)` x² - x +
`(7)/(2)`

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) = (1, 3 ), thus

y = a(x - 1)² + 3

To find a substitute (- 1, 5) into the equation

5 = a(- 1 - 1)² + 3 ( subtract 3 from both sides )

2 = 4a ( divide both sides by 4 )

a =
`(1)/(2)` , thus

y =
`(1)/(2)` (x - 1)² + 3 ← expand factor using FOIL

y =
`(1)/(2)` (x² - 2x + 1) + 3 ← distribute parenthesis

=
`(1)/(2)` x² - x +
`(1)/(2)` + 3

=
`(1)/(2)` x² - x +
`(7)/(2)`