Question

Re-write the quadratic function below in standard form: y=-(x-1)(x-3)

a) y = -x² + 4x - 3
b) y = -x² - 4x - 3
c) y = -x² + 4x + 3
d) y = -x² - 4x + 3

Answer 1

The quadratic function y = -(x-1)(x-3) is re-written in standard form by expanding and distributing the negative sign, resulting in y = -x² + 4x - 3, which corresponds to option (a).

Step-by-step explanation:

The student's question concerns re-writing a quadratic function in standard form. The given quadratic function is y = -(x-1)(x-3). To rewrite this function in standard form, which is y = ax² + bx + c, we need to expand the given expression:

y = -[(x² - 3x) - (x - 3)]
y = -[x² - 3x - x + 3]
y = -[x² - 4x + 3]

When we distribute the negative sign, the function becomes:

y = -x² + 4x - 3

Therefore, the quadratic function in standard form is y = -x² + 4x - 3. The correct answer is option (a).