Find the value of P such that the vertex of `y=x^2+2px+13` is 4 units above the x-axis. (a) `+-2` (b) 4 (c) `+-3` (d) 5

Explanation

To find the value of \( p \) such that the vertex of the parabola \( y = x^2 + 2px + 13 \) is 4 units above the x-axis, we can follow these steps:

### Step 1: Identify the vertex of the parabola
The standard form of a parabola is given by \( y = ax^2 + bx + c \). The vertex \( (h, k) \) of the parabola can be found using the formula:
\[ h = -\frac{b}{2a} \]
In our case, \( a = 1 \) and \( b = 2p \). Therefore,
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