Question: Question 8 (2 points) Determine the equation of the parabola in standard form. \[…

Question 8 (2 points)

Determine the equation of the parabola in standard form.

\[ \begin{array}{c|c} x & y \\ \hline -5 & -4 \\ -4 & -3 \\ -3 & -2 \\ -2 & -1 \\ -1 & 0 \\ 0 & 1 \\ 1 & 2 \\ 2 & 3 \\ 3 & 4 \\ 4 & 5 \\ 5 & 6 \\ \end{array} \]

(-1, 0)

(1, -4)

Solution

Identify the vertex of the parabola. The equation of a parabola in vertex form is: \[ y = a(x - h)^2 + k \] Substitute the vertex coordinates \((1, -4)\): \[ y = a(x - 1)^2 - 4 \] Use the point \((-1, 0)\) to find the value of \(a\): \[ 0 = a(-1 - 1)^2 - 4 \] Simplify and solve for \(a\): \[ 0 = 4a - 4 \] \[ 4a = 4 \] \[ a = 1 \] Substitute \(a = 1\) back into the equation: \[ y = (x - 1)^2 - 4 \]