Question

use this function to answer three following questionsA quadratic function is defined by g(x) = (x+4)² + 7.1. what is the vertex of the graph of function f?2. does the vertex represent the minimum value or the maximum value of the function? one sentence explaining please 3. if you were to shift this graph 5 units down from where it is not, what would be the equation represented by the new graph

Answer 1

1) The vertex is (-4,7)

2) The vertex represents a minimum value

3) The new equation after shifting is;

`g(x)=(x+4)^2+2`

Here, we want to solve the attached questions using the information given

a) Here, we want to get the vertex of the quadratic function

To get this, we need to have the quadratic equation in the vertex from

The vertex form is;

`\begin{gathered} y\text{ = }a(x-h)^2\text{ + k} \\ \\ \text{where vertex is (h,k)} \end{gathered}`

Comparing this with what we have, as we already have the function in the vertex form, the vertex of the function is the point;

`(-4,7)`

b) The vertex represents a minimum value as the value of a is positive, and a positive a value indicates a minimum point

c) Here, we want to shift the graph 5 units down

By shifting 5 units down, we are having a change in the y-axis value

Shifting down means we are moving towards the negative y-axis. Hence, we are going to subtract the value from the whole of the equation

Thus, we have this as;

`\begin{gathered} g(x)=(x+4)^2\text{ + 7-5} \\ g(x)=(x+4)^2+2 \end{gathered}`