Question

What can be said about the discriminant of the graph below?

Answer 1

C. The discriminant is negative, so there are no solutions.

Explanation:

We see that the given figure is a graph of a parabola.

The equation of the given parabola is
`y=(x-3)^(2)+1`.

Simplifying the equation in quadratic form, we get,

The equation is
`y=(x-3)^(2)+1` i.e.
`y=x^(2)+9-6x+1` i.e.
`y=x^(2)-6x+10`.

We know that the discriminant of a quadratic equation
`ax^(2)+bx+c=0` is given by
`D=b^(2)-4ac`

So, from the equation
`x^(2)-6x+10=0`, we have,

a = 1, b = -6 and c = 10

Thus, the discriminant is
`D=(-6)^(2)-4* 1* 10`

i.e.
`D=36-40`

i.e.
`D=-4`

So, the discriminant is -4 i.e. negative.

Hence, as the discriminant is negative, there are no solutions.