Question

Find the equation of the parabola where y_intercept is 7 and vertex is (2,1)​

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) = (2, 1), thus

y = a(x - 2)² + 1

To find a substitute (0, 7) into the equation

7 = a(0 - 2)² + 1

7 = 4a + 1 ( subtract 1 from both sides )

6 = 4a ( divide both sides by 4 )

a =
`(3)/(2)`

y =
`(3)/(2)`(x - 2)² + 1 ← in vertex form

Expand and simplify

y =
`(3)/(2)`(x² - 4x + 4) + 1

=
`(3)/(2)` x² - 6x + 6x + 1

y =
`(3)/(2)` x² - 6x + 7 ← in standard form