Question

Re-write the quadratic function below in Standard Form y = 2(x - 5)(x + 7)​

Answer 1

To rewrite the quadratic function y = 2(x - 5)(x + 7) in Standard Form, we expand the product of the binomials and multiply through by the coefficient 2, resulting in y = 2x^2 + 4x - 70.

Step-by-step explanation:

The given quadratic function is y = 2(x - 5)(x + 7). To rewrite this function in Standard Form, which is represented as y = ax^2 + bx + c, we need to expand the parentheses and combine like terms.

Let's start by expanding the given expression:

1. Multiply the binomials: (x - 5)(x + 7) to get x^2 + 7x - 5x - 35.
2. Combine like terms: x^2 + 2x - 35.
3. Finally, multiply through by the coefficient 2: 2x^2 + 4x - 70.

The Standard Form of the quadratic function is therefore y = 2x^2 + 4x - 70.