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
whats the right answer
The correct answer is "two real solutions." This can be determined by looking at the shape of the parabola on the graph. Since the parabola opens upward, it will intersect the x-axis at two points, resulting in two real solutions.
Based on the graph and the given points, the quadratic function has two real solutions.
To determine the number of real solutions for a quadratic function, we can look at the vertex of the parabola. In this case, the vertex is given as (-2, -4).
Since the parabola opens upward and its vertex lies below the x-axis, there are two possibilities: either the parabola intersects the x-axis two times (two real solutions) or it doesn't intersect the x-axis at all (no real solutions).
Looking at the graph, we can see that the parabola intersects the x-axis at the points (-4, 0) and (0, 0), which means there are two real solutions.
Therefore, the correct answer is "two real solutions."