The function of the arch window is a quadratic function, and the length of the base of the window is 3.5 units
How to determine the length of the base?
The function of the arch window is given as:
h(x) = -4x² + 10x - 6
Set the function to 0
-4x² + 10x - 6 = 0
Divide through by -2
2x² - 5x + 3 = 0
Expand the function
2x² + x - 6x + 3 = 0
Factorize the function
x(2x + 1) - 3(2x + 1) = 0
Factor out 2x + 1
(x - 3)(2x + 1) = 0
Expand
x - 3 = 0 or 2x + 1 = 0
Solve for x
x = 3 or x = -0.5
Since, the base of the window is on the x-axis.
It means that the difference between the x-intercepts represents the length of the window base.
So, we have:
Base = |-0.5 - 3|
Evaluate
Base = 3.5
Hence, the length of the base of the window is 3.5 units
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