Question

Given the function and the graph below, please answer the following:

Answer 1

The given quadratic function is

`f(x)=(-x-1)^2+3`

It represented graphically by an upward parabola

Since the parabola is upward, then it has a minimum vertex

From the graph, the minimum vertex is (-1, 3)

Then let us answer the questions

Maximum point: None

Minimum point: (-1, 3)

To find f(-5), substitute x by 5 in the function above

`\begin{gathered} f(-5)=(--5-1)^2+3 \\ f(-5)=(5-1)^2+3 \\ f(-5)=(4)^2+3 \\ f(-5)=16+3 \\ f(-5)=19 \end{gathered}`

To find f(6), substitute x by 6 in the function above

`\begin{gathered} f(6)=(-6-1)^2+3 \\ f(6)=(-7)^2+3 \\ f(6)=49+3 \\ f(6)=52 \end{gathered}`

The answers:

f(-5) = 19

f(6) = 52