To determine the complete vertex form of the equation based on the given point and the fact that the graph curves upward, we can use the vertex form of a quadratic equation, which is:
\[ y = a(x - h)^2 + k \]
where \((h, k)\) is the vertex of the parabola. In this case, we know that the vertex is at the point \((2, k)\), and since the curve opens upward, \(a\) must be positive.
Given that the point \((2, -14)\) is on the graph, we can see that when \(x = 2\), \(y = -14\). This means that \(k = -14\).
Therefore, we can substitute \(h = 2\) and \(k = -14\) into the vertex form:
\[ y = a(x - 2)^2 - 14 \]
Now we still need the value of \(a\). However, since the problem does not provide additional points to determine the value of \(a\), we will leave it as \(a\), where \(a > 0\).
Thus, the equation in vertex form is:
\[ y = a(x - 2)^2 - 14 \]
where \(a\) is a positive constant. If you have more information about another point on the graph, we could find a specific value for \(a\).
1 answer