For what values of x is f(x)>0?
1 answer:
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Answer:
7√3
Step-by-step explanation:
We can use pythagoreans theorem to solve this
Since, we know one side, and the hypotenuse, we can solve for the other side.
Pythagoreans theorem: a²+b²=c²
Where a and b are two sides, and c is the hypotenuse (the side opposite of the right angle)
In this triangle, 7 is the side, and 14 is the hypotenuse.
I will plug in the values into pythagoreans theorem, and then simplify:
So x = 7√3
This is the equation of an upside down parabola, so the maximum height will be at the vertex. To find the vertex, we'll use the formula for the x-coordinate and then solve for the y-coordinate.
Plugging this into the given formula:
Since it asks us to round, the maximum height would be 20 yards. To find how far the football travels in total, we need to set the equation equal to 0 and find the roots:
Then by the zero product property (or the no zero divisors rule), we have:
(this is the x value where the ball is kicked from)
So the ball travels 51 yards in total.
Plugging this into the given formula:
Since it asks us to round, the maximum height would be 20 yards. To find how far the football travels in total, we need to set the equation equal to 0 and find the roots:
Then by the zero product property (or the no zero divisors rule), we have:
So the ball travels 51 yards in total.