Question

Write the equation of parabola that has vertex (9,7) and passes through point (3,8).

Answer 1

see explanation

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) = (9, 7), thus

y = a(x - 9)² + 7

To find a substitute (3, 8) into the equation

8 = a(3 - 9)² + 7

8 = 36a + 7 ( subtract 7 from both sides )

36a = 1 ( divide both sides by 36 )

a =
`(1)/(36)`

y =
`(1)/(36)`(x - 9)² + 7 ← in vertex form

Expanding the factor and simplifying

y =
`(1)/(36)`(x² - 18x + 81) + 7

=
`(1)/(36)` x² -
`(1)/(2)` x +
`(9)/(4)` + 7

=
`(1)/(36)` x² -
`(1)/(2)` x +
`(37)/(4)` ← in standard form