Question

question 4 of 10
at how many points does the graph of the function below intersect the x
axis?
y=2x²-7x+7

a. 0
b. 1
c. 2

Explanation:

Step1: Recall the discriminant formula for a quadratic function \(y = ax^2 + bx + c\), which is \(\Delta = b^2 - 4ac\). The number of \(x\)-axis intersections is determined by the discriminant: if \(\Delta>0\), 2 points; \(\Delta = 0\), 1 point; \(\Delta<0\), 0 points.

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

Step2: Calculate the discriminant \(\Delta\).

$$
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Since \(\Delta=-7<0\), the quadratic function has no real roots, meaning its graph intersects the \(x\)-axis at 0 points.

Answer:

A. 0