Question

Find the vertex of the given function f(x) = |x - 5| + 10. The vertex is at:

a) (0, 15)
b) (5, 10)
c) (5, 15)
d) (0, 10)

Answer 1

The vertex of the given function f(x) = |x - 5| + 10 is (5/2, 10).

Step-by-step explanation:

The vertex of a quadratic function in the form f(x) = ax^2 + bx + c can be found using the formula: x = -b / (2a). In this case, the function f(x) = |x - 5| + 10 can be rewritten as f(x) = 1 * |x - 5| + 10. Therefore, a = 1 and b = -5. Plugging these values into the formula, we get x = -(-5) / (2 * 1) = 5 / 2. Substituting this value back into the function, we can find the y-coordinate of the vertex by evaluating f(5/2) = |5/2 - 5| + 10 = |0| + 10 = 10. So, the vertex of the function is (5/2, 10).