Write an equation of the parabola that passes through the point (1,5) and has x-intercepts 2 and 6 . An equation of the parabola is y

Answer 1

By the symmetry of the parabola, the x-coordinate, h, of the vertex lies halfway between the x-intercepts.

So, h = 4.

The vertex form of the parabola is y = a(x - h)² + k

So, y = a(x - 4)² + k

Since (1,5) is on the graph, 5 = 9a + k

Since (2,0) is on the graph, 0 = 4a + k

Solve for a and k.

Answer 2

y = (x-2) * (x-6) has x-intercepts at 2 and 6.

To make sure the function goes through the point (1,5), let us add a coefficient a and solve for a when for x=1 and y=5:

y = a * (x-2) * (x-6)

( 5 ) = a * ( ( 1 ) - 2 ) * ( ( 1 ) - 6 )

5 = a * ( -1 ) * ( - 5 )

5 = 5 * a

a = 1

In standard form,

y = x² -8x + 12.

Here is the graph, verifying that all conditions are met:

https://www.desmos.com/calculator/sl4lmkhkwz