Answer :
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 graph of this function opens up if the coefficient "a" is positive and down if it is negative,
- The axis of symmetry is parallel to the y axis, passing through the vertex of the function
- The vertex of the parabola corresponds to the maximum or minimum of the curve
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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