Question
How many real solutions does g(x) = -1.6 - 0.2x^2 have, based on its graph?
Answers
Answered by
GPT 3.5
The number of real solutions of a quadratic equation can be determined by analyzing the graph of the quadratic function.
The graph of a quadratic function is a parabola. The number of real solutions depends on the number of times the parabola intersects or touches the x-axis.
For the given function g(x) = -1.6 - 0.2x^2, the coefficient of x^2 is negative (-0.2), indicating that the parabola opens downwards.
Since the parabola opens downwards, it will intersect the x-axis in two places, or it may touch the x-axis at a single point.
Therefore, the quadratic equation g(x) = -1.6 - 0.2x^2 has 2 real solutions based on its graph.
The graph of a quadratic function is a parabola. The number of real solutions depends on the number of times the parabola intersects or touches the x-axis.
For the given function g(x) = -1.6 - 0.2x^2, the coefficient of x^2 is negative (-0.2), indicating that the parabola opens downwards.
Since the parabola opens downwards, it will intersect the x-axis in two places, or it may touch the x-axis at a single point.
Therefore, the quadratic equation g(x) = -1.6 - 0.2x^2 has 2 real solutions based on its graph.