A flying squirrel jumped from a tree branch and floated to the ground. The squirrel's height (in meters above the ground) \( t \) seconds after jumping is modeled by \( h(t)=-2 t^{2}+4 t+30 \) Suppose we want to know the height of the squirrel above the ground at its highest point. 1) Rewrite the function in a different form (factored or vertex) where the answer appears as a number in the equation. \( h(t)=\square \mp \)

To find the height of the flying squirrel at its highest point, we can rewrite the quadratic function in vertex form. The vertex form of a quadratic function is given by \( h(t) = a(t - h)^2 + k \), where \((h, k)\) is the vertex. To find the vertex, we can use the formula \( t = -\frac{b}{2a} \). Applying this to our function, where \( a = -2 \) and \( b = 4 \): \[ t = -\frac{4}{2 \times -2} = 1 \] Now we substitute \( t = 1 \) back into the original height function to find the maximum height: \[ h(1) = -2(1)^2 + 4(1) + 30 = 32 \] Now we can express it in the vertex form: \[ h(t) = -2(t - 1)^2 + 32 \] In this equation, the highest point of the squirrel’s jump is clearly shown, with the answer being: \[ h(t) = 32 \mp \]