Graph the equation y=x2+4 . How does the graph interact with the x-axis?(1 point) Responses The graph touches the x-axis at one point. The graph touches the x-axis at one point. The graph crosses the x-axis at two points. The graph crosses the x-axis at two points. The graph does not cross or touch the x-axis. The graph does not cross or touch the x-axis. Question 2 What does this tell us about the number and nature of the solutions for this equation?(1 point) Responses The equation has 1 real solution with multiplicity The equation has 1 real solution with multiplicity The equation has 1 real solution and 1 complex solution The equation has 1 real solution and 1 complex solution The equation has 2 real solutions The equation has 2 real solutions The equation has 2 complex solutions The equation has 2 complex solutions It is impossible to determine how many solutions there will be based on the graph alone

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GPT-4o mini · Answer

To analyze the equation $ y = x^2 + 4 $, we can first look at how it interacts with the x-axis. 1. **Graph Interaction with the X-axis:** The equation $ y = x^2 + 4 $ is a parabola that opens upwards. To find when it intersects the x-axis, we set $ y = 0 $: $$ 0 = x^2 + 4 $$ Solving for $ x^2 $: $$ x^2 = -4 $$ This equation has no real solutions since $ x^2 $ cannot be negative. Therefore, the graph does not cross or touch the x-axis. **Answer:** The graph does not cross or touch the x-axis. 2. **Nature of the Solutions:** Since the graph does not touch or cross the x-axis, this indicates that the equation has no real solutions. Instead, the solutions are complex. **Answer:** The equation has 2 complex solutions.