Question
Question Re-write the quadratic function below in Standard Form \( y=6(x-4)^{2}-6 \)
Ask by Carter Gordon. in the United States
Feb 19,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The quadratic function in standard form is \( y = 6x^{2} - 48x + 90 \).
Solution
Simplify the expression by following steps:
- step0: Subtract the terms:
\(6\left(x-4\right)^{2}-6\)
- step1: Expand the expression:
\(6x^{2}-48x+96-6\)
- step2: Subtract the numbers:
\(6x^{2}-48x+90\)
To rewrite the quadratic function \( y = 6(x-4)^{2} - 6 \) in standard form, we first expand the expression.
1. Start with the given function:
\[
y = 6(x-4)^{2} - 6
\]
2. Expand \( (x-4)^{2} \):
\[
(x-4)^{2} = x^{2} - 8x + 16
\]
3. Substitute this back into the equation:
\[
y = 6(x^{2} - 8x + 16) - 6
\]
4. Distribute the 6:
\[
y = 6x^{2} - 48x + 96 - 6
\]
5. Combine like terms:
\[
y = 6x^{2} - 48x + 90
\]
Thus, the quadratic function in standard form is:
\[
y = 6x^{2} - 48x + 90
\]
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Bonus Knowledge
To convert the quadratic function \( y = 6(x-4)^{2} - 6 \) into standard form, we first expand the equation. We can start by expanding \( (x-4)^{2} \), which gives us \( x^{2} - 8x + 16 \). Next, substitute this back into the equation: \[ y = 6(x^{2} - 8x + 16) - 6 \] This simplifies to: \[ y = 6x^{2} - 48x + 96 - 6 \\ y = 6x^{2} - 48x + 90 \] Thus, the standard form of the quadratic function is \( y = 6x^{2} - 48x + 90 \). Happy quadratic rewriting!
