The graph shows a quadratic function from -10 to 10 on the x and y axes. Points on the graph include (-5, 5), (-3, -3), (-2, -4), (-1, -3), and (1, 5).A graph is shown with the x-axis labeled negative 10 to 10 in increments of 1 and the y-axis labeled negative 10 to 10 in increments of 1. A parabola is shown opening upward with vertex left parenthesis negative 2 comma negative 4 right parenthesis and connecting the points left parenthesis negative 4 comma 0 right parenthesis and left parenthesis 0 comma 0 right parenthesis.
How many real solutions does the function shown on the graph have?
(1 point)
Responses
no real solutions
no real solutions
one real solution
one real solution
two real solutions
two real solutions
cannot be determined
From the information given, we can see that the quadratic function opens upward (since the parabola intersects the x-axis at two different points).
Therefore, the quadratic function will have two real solutions.
To determine the number of real solutions a quadratic function has, we can look at the vertex and the direction of the parabola.
In the given graph, the vertex of the parabola is at (-2, -4), and the parabola is opening upward.
Since the parabola opens upward, it means the quadratic function has a minimum value at the vertex.
A quadratic function can have zero, one, or two real solutions based on the position of the vertex and the direction of the parabola.
Since the parabola is opening upward, it means that the vertex represents the minimum value of the function, and there are no real solutions. Thus, the answer is "no real solutions".