# Write A Quadratic Function From Its Zeros With Leading Coefficient 1 Worksheet

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To write a quadratic function when you know its zeros (where the function equals zero), you use those zeros to create the equation. For example, if the zeros are $$p$$ and $$q$$, the function can be written as $$y = (x - p)(x - q)$$. This form directly gives you the quadratic equation without needing any extra information. Use these worksheets to enhance your analytical skills.

Algebra 2

## How Will This Worksheet on “Write a Quadratic Function from Its Zeros with Leading Coefficient 1” Benefit Your Student's Learning?

• Reinforce understanding of quadratic function roots (zeros).
• Develop factoring skills for quadratic expressions.
• Enhance critical thinking through problem-solving.
• Connect abstract math concepts to real-world Applications.
• Build foundational knowledge for advanced algebra topics.
• Foster self-directed learning and problem-solving confidence.
• Prepare for assessments with quadratic function-related questions.
• Improve graphical interpretation skills of quadratic functions.

## How to Write a Quadratic Function from Its Zeros with Leading Coefficient 1?

• A quadratic function with zeros p and q can be expressed in factored form as (x−p)(x−q).
• Multiply the factors to expand the quadratic function: (x−p)(x−q)=x^2−(p+q)x+pq.
• Therefore, the quadratic function with zeros p and q and leading coefficient 1, is  y=x^2−(p+q)x+pq.

## Solved Example

Q. Write a quadratic function with zeros $5$ and $-5$.$\newline$Write your answer using the variable $x$ and in standard form with a leading coefficient of $1$.$\newline$$g(x) =$ ______
Solution:
1. Zeroes Identification: Zeroes of the function: $5$ and $-5$. $\newline$Identify the linear factors using the zeros.$\newline$If $5$ is a zero, then $(x - 5)$ is a factor.$\newline$If $-5$ is a zero, then $(x + 5)$ is a factor.
2. Linear Factors: Leading coefficient: $1$.$\newline$Linear factors: $(x - 5)$ and $(x + 5)$.$\newline$The quadratic function in factored form is $f(x) = (x - 5)(x + 5)$.
3. Factored Form: Expand the factored form to get the standard form. $f(x) = (x - 5)(x + 5) = x^2 + 5x - 5x - 25$.
4. Expand and Simplify: Combine like terms.$\newline$$f(x) = x^2 - 25$.

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