Find the Discriminant f(x)=-4x^2+12x-9

$f (x) = - 4 x^{2} + 12 x - 9$

Step 1

The discriminant of a quadratic is the expression inside the radical of the quadratic formula.

$b^{2} - 4 (a c)$

Step 2

Substitute in the values of $a$ , $b$ , and $c$ .

$12^{2} - 4 (- 4 \cdot - 9)$

Step 3

Evaluate the result to find the discriminant.

Simplify each term.

Raise $12$ to the power of $2$ .

$144 - 4 (- 4 \cdot - 9)$

Multiply $- 4 (- 4 \cdot - 9)$ .

Multiply $- 4$ by $- 9$ .

$144 - 4 \cdot 36$

Multiply $- 4$ by $36$ .

$144 - 144$

Subtract $144$ from $144$ .

$0$