Question

question 6 of 10
at how many points does the graph of the function below intersect the x - axis?
$y = 2x^2 - 7x + 7$
a. 1
b. 0
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 intercepts; if \( D = 0 \), there is 1 intercept; if \( D<0 \), there are 0 intercepts.

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

For the function \( y = 2x^2 - 7x + 7 \), we have \( a = 2 \), \( b=-7 \), and \( c = 7 \).

Step3: Calculate the discriminant

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

$$\begin{align*} D&=(-7)^2 - 4\times2\times7\\ &= 49- 56\\ &=-7 \end{align*}$$

\]

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

Since \( D=-7<0 \), the quadratic function has no real roots, which means the graph of the function does not intersect the \( x \)-axis. So the number of intersection points is 0.

Answer:

B. 0