Questions: Find the vertex of the parabola by applying the vertex formula. h(v)=4v^2-14 The vertex is

Solution Steps

To find the vertex of the parabola given by the equation $h(v) = 4v^2 - 14$, we can use the vertex formula for a quadratic function in the form $ax^2 + bx + c$. The vertex $(v, h(v))$ can be found using the formula $v = -\frac{b}{2a}$. In this case, since there is no $v$ term (i.e., $b = 0$), the vertex will be at $v = 0$. We then substitute $v = 0$ back into the equation to find $h(v)$.

The given quadratic function is $h(v) = 4v^2 - 14$. Here, $a = 4$, $b = 0$, and $c = -14$.

Using the vertex formula $v = -\frac{b}{2a}$: $$v = -\frac{0}{2 \cdot 4} = 0$$

Substituting $v = 0$ back into the function to find $h(v)$: $$h(0) = 4(0)^2 - 14 = -14$$

Final Answer