The graph of which function has a minimum located at (4, –3)?

f(x) = x2 + 4x – 11
f(x) = –2x2 + 16x – 35
f(x) = x2 – 4x + 5
f(x) = 2x2 – 16x + 35

None of the options is the answer to the question

Step-by-step explanation:

we know that

The equation of a vertical parabola into vertex form is equal to

where

(h,k) is the vertex of the parabola

case A) we have

In this case the x-coordinate of the vertex will be negative

therefore

case A is not the solution

case B) we have

This case is a vertical parabola open downward (the vertex is a maximum)

The vertex is the point but is not a minimum

see the attached figure

therefore

case B is not the solution

case C) we have

Convert into vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

Complete the square. Remember to balance the equation by adding the same constants to each side

Rewrite as perfect squares

--------> vertex form

The vertex is the point

therefore

case C is not the solution

case D) we have

Convert into vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

Factor the leading coefficient

Complete the square. Remember to balance the equation by adding the same constants to each side

Rewrite as perfect squares

--------> vertex form

The vertex is the point

therefore

case D is not the solution

The answer to the question will be the function