What height in feet does the baseball reach given the equation y = -14x² + 84x + 4?

To determine the maximum height that the baseball reaches given the equation ( y = -14x^2 + 84x + 4 ), we need to analyze the quadratic function. The equation is in the form ( y = ax^2 + bx + c ), where ( a = -14 ), ( b = 84 ), and ( c = 4 ).

The vertex of a parabola defined by a quadratic equation ( y = ax^2 + bx + c ) can be found using the formula for the x-coordinate of the vertex, which is given by ( x = -\frac{b}{2a} ). Substituting in the values from our equation, we have:

[

x = -\frac{84}{2 \cdot -14} = \frac{84}{28} = 3

]

Now, we substitute ( x = 3 ) back into the original equation to find the corresponding height ( y ):

[

y = -14(3)^2 + 84(3) + 4

]

Calculating this step-by-step:

[

y = -14 \cdot 9 + 252 + 4

\