Question

question 24 of 25
when the function below is graphed, how many x-intercepts does it have?
y = 4x² - 12x + 9
a. 0
b. 1
c. 2

Explanation:

Step1: Recall the discriminant formula

For a quadratic function \( y = ax^2 + bx + c \), the discriminant \( D \) is given by \( D = b^2 - 4ac \). The number of \( x \)-intercepts depends on the discriminant: if \( D>0 \), there are 2 intercepts; if \( D = 0 \), there is 1 intercept; if \( D<0 \), there are 0 intercepts.

Step2: Identify \( a \), \( b \), and \( c \)

In the function \( y = 4x^2 - 12x + 9 \), we have \( a = 4 \), \( b=- 12 \), and \( c = 9 \).

Step3: Calculate the discriminant

Substitute the values of \( a \), \( b \), and \( c \) into the discriminant formula:
\[

$$\begin{align*} D&=(-12)^2 - 4\times4\times9\\ &=144 - 144\\ &= 0 \end{align*}$$

\]

Since the discriminant \( D = 0 \), the quadratic function has 1 \( x \)-intercept.

Answer:

B. 1