Question

Instructions: Given the vertex, fill in the vertex form of the quadratic function.

Answer 1

The vertex form of a quadratic function is given by y = a(x-h)^2 + k, where (h, k) represents the coordinates of the vertex. To fill in the vertex form, find the values of a, h, and k using the given quadratic equation. Calculate h = -b/2a and substitute it into the equation to find k. Finally, replace a, h, and k in the vertex form to get the final equation.

Step-by-step explanation:

The vertex form of a quadratic function is given by y = a(x-h)^2 + k, where (h, k) represents the coordinates of the vertex. In this case, we are given the vertex as (h, k) = (-b/2a, f(-b/2a)). So, in order to fill in the vertex form, we need to find the values of a, h, and k.

Given the quadratic function in the form ax^2 + bx + c = 0 where a = 4.90, b = 14.3, and c = -20.0, we can find the vertex using the formula h = -b/2a and substitute the value of h into the equation to find the value of k. Once we have the values of a, h, and k, we can replace them in the vertex form to get the final equation.

Let's calculate the values for a, h, and k:

1. Calculate h: h = -b/2a = -14.3/(2*4.90)
2. Substitute the value of h into the equation to find k: k = f(-b/2a) = f(-14.3/(2*4.90))
3. Replace the values of a, h, and k in the vertex form: y = 4.90(x-h)^2 + k

Now, you can substitute the calculated values of h and k into the vertex form to get the filled vertex form of the quadratic function.

Answer 2

`y=(x+6)^(2)-5`

STEP-BY-STEP EXPLANATION:

A quadratic equation in its vertex form has the following form:

`\begin{gathered} (x-h)^2=y-k \\ \\ y=(x-h)^2+k \end{gathered}`

Where (h, k) is the vertex of the function, therefore, we replace:

`\begin{gathered} y=(x-(-6))^2+(-5) \\ \\ y=\:\left(x+6\right)^2-5 \end{gathered}`