Question

f(x) = -4x^2+12x-9f(x)=−4x 2 +12x−9f, left parenthesis, x, right parenthesis, equals, minus, 4, x, squared, plus, 12, x, minus, 9 What is the value of the discriminant of fff? How many xxx-intercepts does the graph of fff have?

Answer 1

Answer:

The graph has only one x-intercept

Step-by-step explanation:

we have

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

we know that

The discriminant of a quadratic equation of the form

$ax^{2} +bx+c=0$

is equal to

$D=b^{2}-4ac$

in this problem we have

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

so

$a=-4\\b=12\\c=-9$

substitute

$D=12^{2}-4(-4)(-9)$

$D=144-144$

$D=0$

The discriminant is zero

That means ----> The quadratic equation has one real solution

The graph has only one x-intercept