sharon.taylor
sharon.taylor 1h ago • 0 views

Step-by-step examples for writing quadratic equations in Algebra 2

Hey Algebra 2 students! 👋 Having trouble writing quadratic equations? Don't sweat it! This guide + quiz will make you a pro in no time. Let's get started! 🤓
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williams.april6 Dec 27, 2025

📚 Quick Study Guide

    🔍 A quadratic equation is an equation of the form $ax^2 + bx + c = 0$, where $a$, $b$, and $c$ are constants and $a \neq 0$. 💡 To write a quadratic equation given roots $r_1$ and $r_2$, use the form $a(x - r_1)(x - r_2) = 0$. 📝 If given the sum ($S$) and product ($P$) of the roots, the equation can be written as $x^2 - Sx + P = 0$. ➗ Completing the square involves manipulating the equation to form a perfect square trinomial. ➕ The quadratic formula, $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$, can be used to find the roots of any quadratic equation.

🧪 Practice Quiz

  1. What quadratic equation has roots 3 and -2?
    1. $x^2 - x - 6 = 0$
    2. $x^2 + x - 6 = 0$
    3. $x^2 - 5x + 6 = 0$
    4. $x^2 + 5x + 6 = 0$
  2. If the sum of the roots of a quadratic equation is 5 and the product is 6, what is the equation?
    1. $x^2 + 5x + 6 = 0$
    2. $x^2 - 5x + 6 = 0$
    3. $x^2 + 5x - 6 = 0$
    4. $x^2 - 5x - 6 = 0$
  3. Which quadratic equation has a single real root?
    1. $x^2 + 4x + 3 = 0$
    2. $x^2 + 4x + 4 = 0$
    3. $x^2 + 4x + 5 = 0$
    4. $x^2 + 4x = 0$
  4. What is the quadratic equation that passes through the point (0, -8) and has roots 2 and -4?
    1. $x^2 + 2x - 8 = 0$
    2. $x^2 - 2x - 8 = 0$
    3. $2x^2 + 4x - 16 = 0$
    4. $x^2 + 4x - 8 = 0$
  5. Write a quadratic equation where one root is 2 + i.
    1. $x^2 - 4x + 5 = 0$
    2. $x^2 + 4x + 5 = 0$
    3. $x^2 - 4x - 5 = 0$
    4. $x^2 + 4x - 5 = 0$
  6. What quadratic equation has roots that are reciprocals of each other and sum to $\frac{5}{2}$?
    1. $2x^2 - 5x + 2 = 0$
    2. $2x^2 + 5x + 2 = 0$
    3. $x^2 - 5x + 1 = 0$
    4. $x^2 + 5x + 1 = 0$
  7. A rectangle has a length that is 3 more than its width. If the area is 10, what quadratic equation can be used to find the width, $w$?
    1. $w^2 + 3w - 10 = 0$
    2. $w^2 - 3w - 10 = 0$
    3. $w^2 + 3w + 10 = 0$
    4. $w^2 - 3w + 10 = 0$
Click to see Answers
  1. Answer: B
  2. Answer: B
  3. Answer: B
  4. Answer: A
  5. Answer: A
  6. Answer: A
  7. Answer: A

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