Question

A quadratic equation with a negative leading coefficient has a vertex at the point (−5, 6). What can be said about the nature of its roots?

There is 1 repeated root.
There is not enough information given.
There are 2 real and unique roots

Answer 1

A quadratic equation with a negative leading coefficient and a vertex at (-5, 6) will have 2 real and unique roots.

Step-by-step explanation:

A quadratic equation with a negative leading coefficient has a vertex at the point (-5, 6). In a quadratic equation, the vertex represents the highest or lowest point on the graph, which in this case is a minimum point since the leading coefficient is negative. Since the vertex is at (−5, 6), we know that the line of symmetry is x = -5.

Given that the leading coefficient is negative, we can conclude that the quadratic equation has 2 real and unique roots. This is because the parabola opens downwards, intersecting the x-axis at two distinct points.