Question

Using the graph as your guide, complete the following statement.

The discriminant of the function is:
A. Positive
B. Zero
C. Negative

Answer 1

B. Zero

The discriminant, calculated as Δ = b² - 4ac, equals zero, indicating that the quadratic function has a single real root, consistent with the graph where it touches the x-axis at one point.

Step-by-step explanation:

The discriminant of a quadratic function, denoted by Δ, is a crucial parameter in determining the nature of the roots of the quadratic equation. For a quadratic equation in the form
`ax^2` + bx + c = 0, the discriminant is given by the formula Δ = b² - 4ac. In the context of the graph, where the quadratic function intersects the x-axis, the discriminant is a key indicator.

Now, if the discriminant is zero, it implies that the quadratic equation has exactly one real root. This occurs when the parabola associated with the quadratic function just touches the x-axis at a single point. In graphical terms, this corresponds to the vertex of the parabola being exactly on the x-axis. Mathematically, when Δ = 0, the quadratic equation has only one solution, and this is precisely the scenario depicted in the graph.

To calculate the discriminant for the given quadratic function, one would substitute the coefficients (a, b, and c) into the discriminant formula. If the result is zero, it confirms the visual observation from the graph. In this case, the discriminant being zero aligns with the graphical representation of the function touching the x-axis at a single point, supporting the conclusion that the discriminant of the function is indeed zero.

graph: