Question

Find q(x), where q(x) is the rellection across the x-axis of f(x)=x^(2). Write your answer in the form a(x-h)^(2)+k, where a,h, and k are integers

Answer 1

To reflect the function f(x) = x^2 across the x-axis, multiply it by -1, resulting in q(x) = -x^2. In the form a(x-h)^2+k, the equation is written as q(x) = -1(x-0)^2+0, simplifying to q(x) = -x^2.

Step-by-step explanation:

To find the function q(x) that represents the reflection of f(x) = x2 across the x-axis, we simply multiply f(x) by -1. This is because reflecting a function across the x-axis inverts its y-values. Therefore, the reflection of f(x) would be q(x) = -x2.

Expressing q(x) in the form a(x-h)2+k, where a, h, and k are integers, we can see that a is -1 (as it's the coefficient that reflects the graph across the x-axis), h is 0 (since the vertex of the parabola is at the origin and thus not horizontally shifted), and k is also 0 (since the vertex is on the x-axis and thus not vertically shifted).

Therefore, the reflected function is q(x) = -1(x-0)2+0 which simplifies to q(x) = -x2.