Question

Which polynomial function could be represented by the graph below?

On a coordinate plane, a parabola opens up. It goes through (2, 0), has a vertex at (3, negative 3), and goes through (4, 0).

Answer 1

f(x) = 3x2 – 18x + 24

Explanation:

just took the test

Answer 2

• f(x) = 3(x - 3)^2 - 3

Explanation:

Let the base function be

• f(x) = ax^2

It has the vertex at (3, -3), so it is translated 3 units right and 3 units down:

• f(x) = a(x - 3)^2 - 3

It has zero's at (2, 0) and (4, 0)

Substitute and solve for a:

• a(x - 3)^2 - 3 = 0
• a(2 - 3)^2 = 3
• a = 3

or

• a(4 - 3)^2 - 3 = 0
• a = 3

So the function is:

• f(x) = 3(x - 3)^2 - 3

See the attached