True of False? The point (4, 14) is on the curve `y=x^(2)-2`.

Answer

To determine whether the point (4, 14) is on the curve defined by the equation \( y = x^2 - 2 \), we can follow these steps:

### Step 1: Identify the curve equation
The equation of the curve is given as:
\[ y = x^2 - 2 \]

### Step 2: Identify the coordinates of the point
The point we need to check is (4, 14). Here, the x-coordinate is 4 and the y-coordinate is 14.

### Step 3: Substitute the x-coordinate into the curve equation
We will substitute \( x = 4 \) into the equation of the curve to find the corresponding y-value:
\[ y = 4^2 - 2 \]

### Step 4: Calculate the value of y
Now we calculate:
\[ y = 16 - 2 = 14 \]

### Step 5: Compare the calculated y-value with the y-coordinate of the point
We found that when \( x = 4 \), \( y = 14 \). The y-coordinate of the point (4, 14) is also 14.

### Conclusion
Since the calculated y-value (14) matches the y-coordinate of the point (14), we conclude that the point (4, 14) lies on the curve \( y = x^2 - 2 \).

Thus, the statement is **True**.

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