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

Transcript text: Find the vertex of the parabola by applying the vertex formula. \[ h(v)=4 v^{2}-14 \] The vertex is $\square$

Solution

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) $.

Step 1: Identify the Quadratic Function

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

Step 2: Calculate the Vertex $ v $

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

Step 3: Calculate $ h(v) $

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