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?
Answer: Among the given equations, the axis of symmetry of y = x2 + 2 is x = 0.
Let's understand the solution in detail.
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.