Question
Question Re-write the quadratic function below in Standard Form \[ y=5(x-2)^{2}-4 \] Answer Attempt 1 out of 2 \( y=\square \) Submit Answer
Ask by Chavez Mills. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( y = 5x^2 - 20x + 16 \)
Solution
1. Begin with the given function:
\[
y=5(x-2)^2-4
\]
2. Expand the squared term:
\[
(x-2)^2 = x^2 - 4x + 4
\]
3. Multiply the expanded form by 5:
\[
5(x^2 - 4x + 4)= 5x^2 - 20x + 20
\]
4. Substitute back to get:
\[
y = 5x^2 - 20x + 20 - 4
\]
5. Simplify by combining like terms:
\[
y = 5x^2 - 20x + 16
\]
Final answer:
\[
y = 5x^2 - 20x + 16
\]
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Beyond the Answer
To rewrite the quadratic function \( y=5(x-2)^{2}-4 \) in standard form, start by expanding the squared term. This gives you \( y = 5((x-2)(x-2)) - 4 \), which simplifies to \( y = 5(x^2 - 4x + 4) - 4 \). Now distribute the 5: \( y = 5x^2 - 20x + 20 - 4 \). Finally, combine like terms to arrive at the standard form: \( y = 5x^2 - 20x + 16 \). So, the answer in standard form is \( y=5x^2-20x+16 \).
