Question

Why is f(x) = (3x + 5)² + $ not the vertex form of f(x) = 9x² + 2x + 1?

a) Some of the terms are tions instead of integers.
b) The expression has a constant outside of the squared term.
c) The expression is not the product of two binomials.
d) The variable x has a coefficient.

Answer 1

The expression is not in the correct form for the vertex form of the given quadratic equation.

Step-by-step explanation:

The given equation, f(x) = (3x + 5)² + $, is not the vertex form of f(x) = 9x² + 2x + 1 because it violates several conditions:

1. It has a constant outside of the squared term, which is not allowed in the vertex form.
2. The expression does not represent the product of two binomials, as required in the vertex form.
3. The variable 'x' has a coefficient of 3, which is also not allowed in the vertex form.

Therefore, the correct vertex form of f(x) = 9x² + 2x + 1 is not f(x) = (3x + 5)² + $.