The height y (in feet)of a ball that you throw is given by $y = - \frac { 1 } { 180 } x ^ { 2 } + x + 6$ where x is the horizontal distance (in feet)from where you release the ball. How high is the ball when it reaches its maximum height?
A) 90 feet
B) 51 feet
C) 102 feet
D) 6 feet
E) 70 feet

Question

The height y (in feet)of a ball that you throw is given by $y = - \frac { 1 } { 180 } x ^ { 2 } + x + 6$ where x is the horizontal distance (in feet)from where you release the ball. How high is the ball when it reaches its maximum height?
A) 90  feet
B) 51 feet
C) 102 feet
D) 6 feet
E) 70 feet

Quizplus · Accepted Answer

To find the maximum height, we need to find the vertex of the parabolic function. The x-coordinate of the vertex is given by $\frac{-b}{2a}$ where $a$ and $b$ are the coefficients of the quadratic term and the linear term, respectively. Plugging in the values from the given equation, we have $a = -\frac{1}{180}$ and $b = 1$. Thus, the x-coordinate of the vertex is $\frac{-1}{2\left(-\frac{1}{180}\right)} = 90$. To find the corresponding y-coordinate, we plug this value back into the equation:

$y = -\frac{1}{180}(90)^2 + 90 + 6 = 51$

Therefore, the ball reaches its maximum height of 51 feet.

The Height Y (In Feet)of a Ball That You Throw y=−1180x2+x+6y = - \frac { 1 } { 180 } x ^ { 2 } + x + 6y=−1801​x2+x+6

The Height Y (In Feet)of a Ball That You Throw $y = - \frac { 1 } { 180 } x ^ { 2 } + x + 6$