Math Problem Statement
Write a quadratic function with zeros 0 and – 5. Write your answer using the variable x and in standard form with a leading coefficient of 1.
Solution
To write a quadratic function with zeros and , we use the fact that if and are zeros of a quadratic function, the function can be written as:
Where and are the zeros. Here, and .
Substitute the zeros into the equation:
Since the leading coefficient , the equation becomes:
Expand to write it in standard form:
Final Answer:
Do you want me to explain why this works or how to adjust for different coefficients?
Here are 5 related questions to expand your understanding:
- What would the quadratic function look like if the zeros were and ?
- How do you determine the vertex of a quadratic function from its standard form?
- Can you find the axis of symmetry for this quadratic function?
- How does the graph of this quadratic function relate to its factored form?
- How do you find the y-intercept of a quadratic function in standard form?
Tip: To check if a quadratic function has the correct zeros, substitute each zero back into the function and ensure it equals zero!
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Algebra
Quadratic Functions
Factored Form of Polynomials
Formulas
Standard form of a quadratic equation: ax^2 + bx + c = 0
Factored form of a quadratic equation: a(x - r1)(x - r2)
Theorems
Fundamental Theorem of Algebra
Suitable Grade Level
Grades 8-10