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At how many points does the graph of the function below intersect the x-axis? y=4x^2-9x+9

a. 1
b. 0
c. 2

User Hezye
by
8.1k points

1 Answer

3 votes

To find the number of points at which the graph of the function intersects the x-axis, we need to find the roots of the equation:

4x^2 - 9x + 9 = 0

We can use the quadratic formula to find the roots:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

In this case, a = 4, b = -9, and c = 9, so:

x = (-(-9) ± sqrt((-9)^2 - 4(4)(9))) / 2(4)

x = (9 ± sqrt(81 - 144)) / 8

x = (9 ± sqrt(-63)) / 8

Since the discriminant is negative, the roots are complex and the graph does not intersect the x-axis. Therefore, the answer is b. 0.

User Guy Korland
by
7.3k points

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