Math Problem Statement

Solve quadratic equations using the quadratic formula and match the solutions with the provided code key to decode a riddle: 'What is the difference between a Train conductor and a Math teacher?'

Solution

This worksheet is focused on solving quadratic equations using the quadratic formula. Based on the image, students are required to solve the equations and match the solutions with the corresponding letters provided in the "Code Key" section. The quadratic formula for solving equations of the form ax2+bx+c=0ax^2 + bx + c = 0 is:

x=b±b24ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

Steps to Solve Each Quadratic Equation:

  1. Identify the coefficients aa, bb, and cc from each quadratic equation.
  2. Substitute them into the quadratic formula to calculate the solutions (roots).
  3. Compare the solutions to the corresponding values in the "Code Key."
  4. Use the letter associated with the solution from the "Code Key" to fill in the boxes below the equation number.

Would you like help solving a specific quadratic equation from this worksheet?

Here are some related questions to help you:

  1. What is the quadratic formula used for?
  2. How do you determine the discriminant from a quadratic equation?
  3. Can all quadratic equations be solved using the quadratic formula?
  4. What are the steps to simplify the expression under the square root?
  5. How do you handle complex solutions when the discriminant is negative?

Tip: When solving quadratic equations, always check the discriminant b24acb^2 - 4ac to know if the roots are real or complex!

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Math Problem Analysis

Mathematical Concepts

Algebra
Quadratic Equations
Quadratic Formula

Formulas

x = (-b ± sqrt(b^2 - 4ac)) / 2a

Theorems

Quadratic Formula

Suitable Grade Level

Grade 9