The graph below represents the function f. f(x)

if g is a quadratic function with a positive leading coefficient and a vertex at (0,3), which statement is true?

А.
The function fintersects the x-axis at two points, and the function g never intersects the x-axis.

B
The function fintersects the x-axis at two points, and the function g intersects the x-axis at only one point.

c.
Both of the functions fand g intersect the x-axis at only one point.

D
Both of the functions fand g intersect the x-axis at exactly two points.

А.

The function f intersects the x-axis at two points, and the function g never intersects the x-axis.

Step-by-step explanation:

In the graph we can see f(x), first let's do some analysis of the graph.

First, f(x) is a quadratic equation: f(x) = a*x^2 + b*x + c.

The arms of the graph go up, so the leading coefficient of f(x) is positive.

The vertex of f(x) is near (-0.5, -2)

The roots are at x = -2 and x = 1. (intersects the x-axis at two points)

Now, we know that:

g(x) has a positive leading coefficient, and a vertex at (0, 3)

As the leading coefficient is positive, the arms go up, and the minimum value will be the value at the vertex, so the minimum value of g(x) is 3, when x = 0.

As the minimum value of y is 3, we can see that the graph never goes to the negative y-axis, so it never intersects the x-axis.

so:

f(x) intersects the x-axis at two points

g(x) does not intersect the x-axis.

The correct option is A.