Math Problem Statement
Solution
The image shows a set of quadratic equations where you are tasked with writing each equation in standard form and then identifying the values of , , and . I will help you with each one step by step.
Standard form of a quadratic equation:
The standard form of a quadratic equation is: where:
- is the coefficient of ,
- is the coefficient of ,
- is the constant term.
Let's work through the equations one by one.
1.
First, expand and simplify the equation: Step 1: Multiply the two binomials: Step 2: Multiply by 6: Step 3: Set the equation equal to 0: Thus, the equation is in standard form: .
2.
Rearrange the terms to get everything on one side of the equation: Thus, the equation is in standard form: .
3.
Rearrange the terms to get the equation equal to 0: Thus, the equation is in standard form: .
- (since there is no -term)
4.
Rearrange the terms to get the equation equal to 0: Thus, the equation is in standard form: .
5.
Rearrange the terms to get the equation equal to 0: Thus, the equation is in standard form: .
Do you want more details or have any further questions?
Here are 5 questions to expand your understanding:
- How can you solve these quadratic equations once they are in standard form?
- Can you explain how to find the roots of a quadratic equation using the quadratic formula?
- What does the discriminant () tell us about the nature of the solutions?
- What other methods can be used to solve quadratic equations apart from factoring and the quadratic formula?
- How would you graph these quadratic functions and determine their key features?
Tip: Always ensure to have the equation in standard form before identifying , , and . This makes further steps like solving or graphing much easier.
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Math Problem Analysis
Mathematical Concepts
Quadratic Equations
Algebra
Formulas
Standard form of quadratic equation ax^2 + bx + c = 0
Theorems
Expansion of binomials
Quadratic formula
Suitable Grade Level
Grades 8-10
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