Question

Re-write the quadratic function below in Standard Form
y=,5(x-3)²+8 5(x−3) 2+8

Answer 1

To rewrite the quadratic function y = 0.5(x - 3)² + 8 in Standard Form, expand the binomial, multiply by 0.5, and combine like terms to obtain y = 0.5x² - 3x + 12.5.

Step-by-step explanation:

The student has asked to rewrite the quadratic function in Standard Form. The function provided is y = 0.5(x - 3)² + 8. To rewrite it in Standard Form, which is y = ax² + bx + c, we need to expand the squared binomial and combine like terms.

Let's do the math:

1. First, apply the exponent to the binomial: (x - 3)² = x² - 6x + 9.
2. Then, multiply the entire binomial by 0.5: 0.5(x² - 6x + 9) = 0.5x² - 3x + 4.5.
3. Finally, add the 8 to complete the transformation: 0.5x² - 3x + 4.5 + 8 = 0.5x² - 3x + 12.5.

So, the quadratic function in Standard Form is y = 0.5x² - 3x + 12.5.