Create a quadratic function with an axis of symmetry x=3 whose graph opens down

f(x) = -2(x - 3)² - 1

Step-by-step explanation:

Every parabola is symmetric about its axis, which means that if it were folded along its axis, the two parts would match. Given x = 3 as the axis of symmetry, then it means that its vertex must have an h value of 3.

Using the vertex form of the quadratic function:

f(x) = a(x - h)²+ k

where:

a  determines whether the graph opens up or down.

(h, k) is the vertex  

Then, we can establish the following quadratic function using the vertex form:

f(x) = -2(x - 3)² - 1

The vertex of this quadratic function is (3, -1).

Attached is a screenshot of the given function.

Hope this helps :)      

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