Question

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

Answer 1

Answer:

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

Step-by-step 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 $D=(-6)^{2}-4\times 1\times 10$

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.