Question

Which is the graph of a quadratic equation that has a negative discriminant?

Answer 1

Answer:

Here's what I get  

Step-by-step explanation:

The formula for a quadratic equation is

ax² + bx + c = 0

The quadratic formula gives the roots:

$x = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a} = \dfrac{-b\pm\sqrt{D}}{2a}$

D is the discriminant.

It tells us the number of roots to the equation — the number of times the graph crosses the x-axis.

$D = \begin{cases}\text{positive} & \quad \text{2 real solutions}\\\text{zero} & \quad \text{1 real solution}\\\text{negative} & \quad \text{0 real solutions}\\\end{cases}$

It doesn't matter if the graph opens upwards or downwards.

If D > 0, the graph crosses the x-axis at two points.

If D = 0, the graph touches the x-axis at one point.

If D < 0, the graph never reaches the x-axis.

Your graph must look like one of the two graphs on the right in the Figure below.