Question

Rewrite the quadratic function f(x)=ax ² +bx+c in vertex form.

A) f(x)=a(x−h) ²+k
B) f(x)=a(x+h) ² +k
C) f(x)=ax ² −b(x−c)
D) f(x)=a(x+c) ² −b

Answer 1

The quadratic function f(x)=ax²+bx+c can be rewritten in vertex form as f(x)=a(x−h)²+k. The correct answer is A) f(x) = a(x - h)² + k.

Step-by-step explanation:

The quadratic function, f(x) = ax² + bx + c, can be rewritten in vertex form as f(x) = a(x - h)² + k. The correct answer is A) f(x) = a(x - h)² + k.

In the vertex form, (h, k) represents the vertex of the parabola. To rewrite the function in vertex form, we need to complete the square.

Here are the steps to rewrite the quadratic function in vertex form:

1. Identify the values of a, b, and c.
2. Find the value of h using the formula h = -b/2a.
3. Substitute the value of h into the equation: f(x) = a(x - (-b/2a))² + c.
4. Simplify the equation to get the final form: f(x) = a(x - h)² + k, where k = c - (b²/4a).