Question

Rewrite the quadratic function f(x)=x²-10x+28 in the standard form f(x)=a(x-h)²+k. What are the values of a,h, and k.

Answer 1

The quadratic function f(x)=x²-10x+28 in the standard form is f(x)=(x-5)²+3. Therefore, the values are a=1, h=5, and k=3.

Step-by-step explanation:

To rewrite the quadratic function f(x)=x²-10x+28 in the standard form f(x)=a(x-h)²+k, we need to complete the square.

1. Start with the original function: f(x) = x² - 10x + 28.
2. Rearrange the quadratic and linear terms: f(x) = (x² - 10x) + 28.
3. Take half of the coefficient of x, which is -10/2 = -5, and square it to get 25.
4. Add and subtract 25 inside the parentheses: f(x) = (x² - 10x + 25 - 25) + 28.
5. Write the perfect square trinomial and the constant terms: f(x) = ((x - 5)² - 25) + 28.
6. Simplify the constants outside the parentheses: f(x) = (x - 5)² + 3.

The quadratic function in standard form is f(x) = (x - 5)² + 3. Therefore, the values of a, h, and k are a = 1, h = 5, and k = 3, respectively.