Question

question 9 of 10
at how many points does the graph of the function below intersect the x-axis?
$y = 25x^2 - 10x + 1$

a. 0
b. 2
c. 1

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.
Here, \(a = 25\), \(b=- 10\), \(c = 1\).

Step2: Calculate the discriminant

Substitute the values of \(a\), \(b\), and \(c\) into the discriminant formula:
\(D=(-10)^2-4\times25\times1\)
\(=100 - 100\)
\(=0\)
Since the discriminant \(D = 0\), the quadratic function has exactly 1 \(x\)-intercept.

Answer:

C. 1