Question
Re-write the quadratic function below in Standard Form \[ y=2(x+5)^{2}-4 \]
Ask by Ford Bates. in the United States
Feb 19,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The quadratic function in standard form is \( y = 2x^{2} + 20x + 46 \).
Solution
Rewrite the function by following steps:
- step0: Rewrite the function:
\(y=2x^{2}+20x+46\)
The quadratic function in standard form is:
\[
y = 2x^{2} + 20x + 46
\]
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Simplify this solution Bonus Knowledge
To rewrite the quadratic function in standard form, start by expanding the expression. The given function is \( y = 2(x + 5)^2 - 4 \). First, expand \( (x + 5)^2 \): \[ (x + 5)^2 = x^2 + 10x + 25. \] Now multiply it by 2: \[ 2(x^2 + 10x + 25) = 2x^2 + 20x + 50. \] Finally, subtract 4: \[ y = 2x^2 + 20x + 50 - 4 = 2x^2 + 20x + 46. \] So, the function in standard form is: \[ y = 2x^2 + 20x + 46. \]
