Question

I: Mar 8 at 1:11pm z Instructions Question 1 1pts What is the min or max value of f(x)=-x^(2)-4x+3

Answer 1

To find the minimum or maximum value of the function f(x)=-x^2-4x+3, we can use a technique called completing the square. The maximum value of the function is -2.

Step-by-step explanation:

To find the minimum or maximum value of the function f(x)=-x^2-4x+3, we can use a technique called completing the square. This involves rewriting the function in vertex form, which allows us to easily determine the maximum or minimum value.

1. First, we rewrite the function in vertex form: -x^2-4x+3 = -(x^2+4x)-3 = -(x^2+4x+4)+1-3 = -(x+2)^2-2
2. The graph of a function in the form y=a(x-h)^2+k is a parabola that opens upwards if a is positive, or opens downwards if a is negative. Since the coefficient of x^2 is -1 in our function, the parabola opens downwards.
3. Therefore, the maximum value of the function is the y-coordinate of the vertex. The vertex of the parabola is at the point (-2,-2), so the maximum value of f(x) is -2.