Question

question 10 of 25
when the function below is graphed, how many x-intercepts does it have?
y = 4x² + 5x + 2

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 is determined by the discriminant: if \( D>0 \), there are 2 \( x \)-intercepts; if \( D = 0 \), there is 1 \( x \)-intercept; if \( D<0 \), there are 0 \( x \)-intercepts.

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

For the function \( y = 4x^2 + 5x + 2 \), we have \( a = 4 \), \( b = 5 \), and \( c = 2 \).

Step3: Calculate the discriminant

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

$$
LATEXBLOCK0
$$

Step4: Determine the number of \( x \)-intercepts

Since \( D=-7<0 \), the quadratic function has no real roots, which means it has 0 \( x \)-intercepts when graphed.

Answer:

A. 0