Question

1. choose at least 2 of the following. fully factor each quadratic equation (write in intercept form). show your work.

\\(y = x^2 + 9x + 18\\)

\\(y = x^2 - 10x - 24\\)

\\(y = x^2 - 10x + 25\\)

Explanation:

⚡ Using what you learned: factoring trinomials

Step 1: Factor the first equation

For \(y = x^2 + 9x + 18\), find two numbers that multiply to \(18\) and add to \(9\). These numbers are \(3\) and \(6\).

$$ y = (x + 3)(x + 6) $$

Step 2: Factor the second equation

For \(y = x^2 - 10x - 24\), find two numbers that multiply to \(-24\) and add to \(-10\). These numbers are \(-12\) and \(2\).

$$ y = (x - 12)(x + 2) $$

Step 3: Factor the third equation

For \(y = x^2 - 10x + 25\), find two numbers that multiply to \(25\) and add to \(-10\). These numbers are \(-5\) and \(-5\).

$$ y = (x - 5)(x - 5) = (x - 5)^2 $$

Answer:

1. \(y = (x + 3)(x + 6)\)
2. \(y = (x - 12)(x + 2)\)
3. \(y = (x - 5)^2\)