The quadratic function f(x) has a vertex at (5,-5) and opens downward.

If g(x) = (x + 5)2 + 5, which statement is true?


A. The axis of symmetry of f(x) is x = 5, and the axis of symmetry of g(x) is x = -5.

B. The axis of symmetry of f(x) is x = -5, and the axis of symmetry of g(x) is x = -5.

C. The axis of symmetry of f(x) is x = 5, and the axis of symmetry of g(x) is x = 5.

D. The axis of symmetry of f(x) is x = -5, and the axis of symmetry of g(x) is x = 5.

Answer:

The correct answer is A.

Step-by-step explanation:

We're told that f(x) has its vertex at 5, -5 and opens downward.  This tells us that it's axis of symmetry is x = 5.

The format of the function g(x) shows us that its axis of symmetry is x = -5.  We're shown this because of the (x + 5)² component.

So the correct answer is A.

Using the properties of the quadratic function we can review the different answers, the correct one is

D. The axis of symmetry of f(x) is x = -5,

the axis of symmetry of g(x) is g(x) = 5.

The quadratic function is a quadratic polynomial that has a parabolic form and a general equation

        g (x) = a x² + bx + c

where a, b, c are the coefficients, x is the independent variable and g the dependent

If the function has real roots it can be written in vertex form

       g (x) = a (x-h) ² + k

where (h, k) are the coordinates of the vertex

The quadratic function has several properties:

The function can be written as a vertex value that cancels the binomial is where the symmetry axis passes

in this case, for the parabola to open downwards, the curve must be:

               g (x) = - (x + 5) ² + 5

this is the expression in vertex form, let's find the value that cancels the binomial,

              x + 5 = 0

              x = -5

at this point where the axis of symmetry passes

The value of the function for this point is

              x = -5

         g (x0 = - (-5 + 5) ² + 5

          g (x) = 5

Using the properties of the quadratic function we can review the different answers, the correct one is

D. The axis of symmetry of f(x) is x = -5, and the axis of symmetry of g(x) is

g(x) = 5

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