11. find the error in the following solution to find the vertex of the function $y = n^2 - 22n + 97$.\n$h =…

11. find the error in the following solution to find the vertex of the function $y = n^2 - 22n + 97$.\n$h = \\frac{-22}{2(1)} = \\frac{-22}{2} = -11$\n$k = (-11)^2 - 22(-11) + 97 = 460$\nvertex: $(-11, 460)$

11. find the error in the following solution to find the vertex of the function $y = n^2 - 22n + 97$.\n$h = \\frac{-22}{2(1)} = \\frac{-22}{2} = -11$\n$k = (-11)^2 - 22(-11) + 97 = 460$\nvertex: $(-11, 460)$

Answer

Explanation:

Step1: Identify coefficients from the quadratic equation

$$a = 1, b = -22, c = 97$$

Step2: Apply the vertex formula for $h$

$$h = -\frac{b}{2a} = -\frac{-22}{2(1)}$$

Step3: Calculate the correct value of $h$

$$h = \frac{22}{2} = 11$$

Step4: Identify the error in the provided solution

The provided solution used $h = \frac{b}{2a}$ instead of $h = -\frac{b}{2a}$, resulting in $h = -11$ instead of $11$.

Answer:

The error is in the calculation of $h$. The formula for the x-coordinate of the vertex is $h = -\frac{b}{2a}$. The provided solution failed to include the negative sign, incorrectly calculating $h = \frac{-22}{2} = -11$ instead of $h = -\frac{-22}{2} = 11$. Consequently, the value of $k$ was also calculated using the incorrect $h$.