Answer:
Disciminant of f = 0
x-intecept = [tex](\frac{3}{2}, 0)[/tex]
Step-by-step explanation:
Given the quadratic function, -4x² + 12x - 9
where a = -4, b = 12, and c = -9
The discriminant, b²- 4ac, is the expression inside the radical (numerator) of the quadratic formula:
[tex]x = \frac{-b +/- \sqrt{b^{2}-4ac} }{2a}[/tex]
The first part of your given problem asks for the discriminant. Substitute the values for a, b, and c:
b²- 4ac = 12² - 4(-4)(-9) = 144 - 144 = 0 → This implies that the quadratic function has one real root.
Therefore, the disciminant of f is 0.
Next, the given problem asks for the x-intercepts. The x-intercept is the point on the graph where it crosses the x-axis. As I mentioned earlier, the function has one real root. Therefore, it means that there is only 1 x-intercept. To find out what the x-intercept is, use the quadratic formula:
[tex]x = \frac{-b +/- \sqrt{b^{2}-4ac} }{2a}[/tex]
[tex]x = \frac{-12 +/- \sqrt{12^{2}-4(-4)(-9)} }{2(-4)}[/tex]
[tex]x = \frac{-12 +/- \sqrt{144 - 144} }{-8}[/tex]
[tex]x = \frac{-12}{-8} = \frac{3}{2}[/tex]
Therefore, the x-intercept is [tex](\frac{3}{2}, 0)[/tex].
