Mathematics: F(x) = -4x2 + 12x – 9 What is the value of the discriminant of f? How many x-intercepts does the graph of f have?

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F(x) = -4x2 + 12x – 9 What is the value of the

2Dgames

29.01.2022

D = 0

The graph has 1 x-intercept

Step-by-step explanation:

Given

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

Required

- Discriminant of f

- Number of x intercepts

Let D represent the discriminant;

D is calculated as thus

D = b^2 - 4ac

Where a, b and c are derived from the following general format;

f(x) = ax^2 + bx +c

By comparing f(x) = ax^2 + bx +c with f(x) = -4x^2 + 12x - 9

We have

$f(x) = f(x)\\ax^2 = -4x^2\\bx = 12x\\c = -9$

Solving further;

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

So, D can now be calculated;

D = b^2 - 4ac becomes

D = 12^2 - 4 * -4 * -9

D = 144 - 144

D = 0

Hence, the discriminant of f is 0

From the value of the discriminant, we can determine the number of x intercepts of the graph;

When D = 0, then; there exists only one x-intercept and it as calculated as thus

$x = \frac{-b}{2a}$

Recall that

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

So, $x = \frac{-b}{2a}$ becomes

$x = \frac{-12}{2 * -4}$

$x = \frac{-12}{-8}$

$x = \frac{12}{8}$

x =1.5

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