Question

Convert y=a(x−4)(x−10) to standard form.

Answer 1

To convert y=a(x-4)(x-10) to standard form, distribute a across the binomials, foil the terms to combine like terms, and then multiply each term by 'a'. This results in the standard form ax² - 14ax + 40a.

Step-by-step explanation:

To convert the equation y=a(x−4)(x−10) to standard form, we need to expand the terms and simplify. The standard form of a quadratic equation is ax² + bx + c.

Let's expand the given equation step by step:

1. Distribute the a across the terms (x−4) and (x−10).
2. FOIL (First, Outside, Inside, Last) the binomials to get a(x² - 10x - 4x + 40).
3. Combine like terms: a(x² - 14x + 40).
4. Multiply each term by a to get the standard form: ax² - 14ax + 40a.

Without an actual value for 'a', we will leave the equation in terms of 'a'.