To find the x-intercepts, we set f(x) = 0 and solve for x:
0 = -0.04(x^2 - 55x - 300)
0 = x^2 - 55x - 300
This is a quadratic equation that can be factored as:
0 = (x - 60)(x + 5)
Setting each factor to zero gives us the x-intercepts:
x = 60 and x = -5
In this context, the x-intercepts represent the points at which the object hits the ground after being launched from the slingshot. The x-intercept of x = 60 means that the object travels 60 feet horizontally before hitting the ground, and the x-intercept of x = -5 means that the object was launched 5 feet behind the slingshot.
To find the y-intercept, we set x = 0 in the function f(x):
f(0) = -0.04(0^2 - 55*0 - 300)
f(0) = -0.04(-300)
f(0) = 12
Therefore, the y-intercept is 12 and it represents the initial height (in feet) of the object when it is launched from the slingshot.
The height (in feet) of an object launched from a slingshot is represented by the function f(x) = - 0.04(x ^ 2 - 55x - 300) , where x is the horizontal distance traveled (in feet) by the object. Find and interpret the x - and y - intercepts in this context. The x-intercept is and represents the blank The y -intercept is and represents the blank
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