Math Problem Statement
Transform each quadratic function in the form y=ax²+ bc+c 1)y-x+5=(x-2)²
Solution
Let's transform the given quadratic equation into the standard form .
Step 1: Expand the squared term
First, expand the right-hand side of the equation: Now, the equation becomes:
Step 2: Simplify the equation
Next, move all terms that are not related to to the right-hand side:
Step 3: Combine like terms
Simplify the expression on the right-hand side:
Final Answer:
The equation in the form is:
Do you need any details or have questions?
Here are 5 questions that could extend the understanding:
- How do you expand binomials like ?
- What is the significance of combining like terms in this transformation?
- Can you graph this quadratic function and interpret its key features (vertex, intercepts)?
- How would completing the square apply to this equation?
- What does the coefficient tell you about the shape of the parabola?
Tip: Always check for like terms when simplifying quadratic equations to avoid errors.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Algebra
Quadratic Equations
Expanding Binomials
Simplification
Formulas
Standard form of a quadratic equation: y = ax^2 + bx + c
Theorems
None directly involved; focuses on algebraic manipulation and simplification
Suitable Grade Level
Grades 8-10