Choose the equation below whose axis of symmetry is x = 0. Is it y = x² + 2x, y = x² − 16x + 58, y = x² + 2 or y = x² − 4x + 2?

Quadratic equations are equations that have a degree equal to two. They are represented as a parabola on the graph. 

Answer: Among the given equations, the axis of symmetry of y = x² + 2 is x = 0.

Let's understand the solution in detail.

Explanation:

To check for the symmetry about x = 0 is the same as to check the symmetry about the y-axis.

If a curve is symmetrical about the y-axis, then it is said to be even.

Hence, we have to check if the curves given follow the relation f(-x) = f(x).

Now, replacing y with f(x):

⇒ If f(x) = x² + 2x, then f(-x) = x² - 2x; hence they are not equal.

⇒ If f(x) = x² − 16x + 58, then f(-x) = x² + 16x + 58; hence, they are not equal.

⇒ If f(x) = x² + 2, then f(-x) = x² + 2, hence, they are equal.

⇒ If f(x) = x² − 4x + 2, then f(-x) = x² + 4x + 2, hence, they are not equal.

Hence, among the given equations, the axis of symmetry of y = x² + 2 is x = 0.