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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?

Respuesta :

calculista

Answer:

The graph has only one x-intercept

Step-by-step explanation:

we have

[tex]f(x)=-4x^2+12x-9[/tex]

we know that

The discriminant of a quadratic equation of the form

[tex]ax^{2} +bx+c=0[/tex]

is equal to

[tex]D=b^{2}-4ac[/tex]

in this problem we have

[tex]f(x)=-4x^2+12x-9[/tex]

so

[tex]a=-4\\b=12\\c=-9[/tex]

substitute

[tex]D=12^{2}-4(-4)(-9)[/tex]

[tex]D=144-144[/tex]

[tex]D=0[/tex]

The discriminant is zero

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

The graph has only one x-intercept

0 and 1 are the correct answers.

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