At how many points does the graph of the function below intersect the x-axis?y = 3x2 - 8x + 8
Question
At how many points does the graph of the function below intersect the x-axis?
y = 3x^2 - 8x + 8
Solution
The graph of the function y = 3x^2 - 8x + 8 intersects the x-axis at the points where y = 0.
To find these points, we set y = 0 and solve for x:
0 = 3x^2 - 8x + 8
This is a quadratic equation, and we can solve it using the quadratic formula:
x = [-b ± sqrt(b^2 - 4ac)] / (2a)
where a = 3, b = -8, and c = 8.
First, calculate the discriminant (b^2 - 4ac):
(-8)^2 - 438 = 64 - 96 = -32
Since the discriminant is negative, there are no real roots for this equation. Therefore, the graph of the function does not intersect the x-axis at any point.
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