Use the discriminant to classify the graph.
A)The graph is a hyperbola.
B)The graph is a ellipse.
C)The graph is a circle.
D)The graph is a line.
E)The graph is a parabola.

Question

Use the discriminant to classify the graph. ​  ​
A)The graph is a hyperbola. 
B)The graph is a ellipse. 
C)The graph is a circle. 
D)The graph is a line. 
E)The graph is a parabola.

Quizplus · Accepted Answer

The discriminant of a quadratic equation in standard form (y = ax^2 + bx + c) is given by b^2 - 4ac. For a parabola, the discriminant is equal to 0. Looking at the given equation, we can see that it is a quadratic, so we can calculate the discriminant: (-6)^2 - 4(5)(-4) = 136. Since the discriminant is not equal to 0, the graph is not a parabola. Therefore, the best choice is E, the graph is a parabola.

Use the Discriminant to Classify the Graph