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, expand and simplify the equation to get y = 2x² + 4x − 70.

Step-by-step explanation:

To rewrite the quadratic function y = 2(x−5)(x+7) in Standard Form, we need to expand the equation and then simplify it. Standard Form of a quadratic function is y = ax² + bx + c.

Let's expand step by step:

1. First, we distribute the 2 into the parentheses: y = 2[(x−5)(x+7)].
2. Next, we use the distributive property (FOIL method) to expand the parentheses: y = 2[x² + 7x − 5x − 35].
3. Combine like terms inside the brackets: y = 2[x² + 2x − 35].
4. Finally, distribute the 2 to every term inside the brackets: y = 2x² + 4x − 70.

Now, the quadratic function is in Standard Form y = 2x² + 4x − 70.