Key Concept: If a point lies on a given line (or curve), then the x- and y-coordinates of that point must satisfy the equation of that line (or curve)

So, let's check each answer choice...

(A) (3, 6)
Plug x = 3 and y = 6 into the given equation y = x² - 3
We get: 6 = 3² - 3
Since the coordinates satisfy the equation of the curve, we know that (3, 6) lies ON the curve

(B) (-3, 6)
Plug x = -3 and y = 6 into the given equation y = x² - 3
We get: 6 = (-3)² - 3
Since the coordinates satisfy the equation of the curve, we know that (-3, 6) lies ON the curve

(C) (0, -3)
We get: -3 = 0² - 3
Since the coordinates satisfy the equation of the curve, we know that (0, -3) lies ON the curve

(D) (-3, 0)
We get: 0 = (-3)² - 3
Since the coordinates DO NOT satisfy the equation of the curve, we know that (-3, 0) does NOT lie on the curve

Answer: D

The problem asks for the point that does not lie on the curve. y = x2 – 3
is the equation of a parabola, but you don’t need to know that fact in order to
answer this question. For each choice, plug in the coordinates for x and y. For
instance, try choice (A):
6 = (3)
2 – 3
6 = 6
Since this is a true statement, choice (A) lies on the curve. The only choice
that yields a false statement when plugged in is choice (D), the correct answer.
For the point (–3, 0) to lie on the curve y = x2 – 3, y needs to equal 0 when –3
is plugged in for x:
y = (–3)2 – 3
y = 9 – 3 = 6
y does not equal 0 when x equals –3, so the point does not lie on the curve.