Question

Select the correct answer. What is the domain of the function represented by the graph? A graph shows an upward parabola on a coordinate plane vertex at (minus 4, minus 4) which intercepts axis at (minus 5, 0), and (minus 3, 0) passes through (minus 3, 1), and (minus 2.5, minus 5). x ≥ 4 x ≤ -2 x ≥ -6 all real numbers

Answer 1

Since the vertex is at (-4,-4) and the parabola opens upward, we know that the function is of the form f(x) = a(x+4)^2 - 4, where "a" is a positive constant.

The fact that the parabola intercepts the x-axis at (-5,0) and (-3,0) tells us that the roots of the quadratic are x = -5 and x = -3. Therefore, the function is equal to zero at x = -5, -3, and -4.

Since the parabola passes through (-3,1), we can use this information to solve for "a". Plugging in x = -3 and y = 1, we get:

1 = a(-3+4)^2 - 4

1 = a - 4

a = 5

So the function is f(x) = 5(x+4)^2 - 4.

The domain of this function is all real numbers, since there are no restrictions on the possible values of x that can be plugged into the quadratic function.

Therefore, the correct answer is: all real numbers.