Answer:
- The x-intercepts are the solutions of the equation.
Explanation:
A quadratic equation may have two different real solutions, two equal real solutions, or two complex (conjugated) solutions.
The graph of a quadratic function with two different real solutions crosses the x-axis at two points, which are the x-intercepts.
The graph of a quadratic function with two equal real solutons touches the x-axis at one point, which is the x-intercept.
The graph of a quadratic function with two complex solutions does not touch or cross the x-axis: it does not have x-intercepts.
Look at the determinant of the equation: it is the amount inside the root:
- b² - 4(a)(c) = (6.42)² - 4(2.475)(-5.238).
That is a positve number ( > 0). When the discriminant is greater than zero, the equation has to different real solutions, which are the x-intercepts of the graph.
Hence, in this case, Cody can use the graph because the x-intercepts are the solutions of the equation.
