New question: A baseball was 2.74 feet above ground when it was hit. It reached a max. height of 116.3ft when it was approx 215.3 ft away from where he hit the ball. The ball lands after travelling a ground distance of approx 433.1 ft.
Find an equation of form y = A(x-h)^2 + k where vertex is (h,k) and constant A is a scaling factor.
So the vertex is (215.3, 116.3).
Plugging in I have
y = A (x-215.3)^2 + 116.3
Using point (0, 2.74), I have
2.74 = A (0-215.3)^2 + 116.3
2.74 = A (46354.09 + 116.3)
2.74 = A 46,470.39
0.000059 = A
**** shouldn't my A be negative to get a hill shape?
Yes. You made a mistake, placing the right parenth ) the right of the 116.3.
A will be negative if you solve
46354 A = 2.74 - 116.3 = -113.56
A = -0.0024498
Check: when x = 433.1,
y = -0.0024498(433.1-215.3)^2+116.3
= -116.2 +116.3 = 0.01
That's close enough.
To find the equation of the parabolic path of the baseball, you are correct that the coefficient A should be negative in order to obtain a "hill" shape. The negative coefficient reflects the fact that the parabola opens downwards (since the ball starts at a higher point and falls downwards).
So, if you plug in the given points (0, 2.74) and (215.3, 116.3) into the equation y = A(x-h)^2 + k, you should get:
2.74 = A(0-215.3)^2 + 116.3
Simplifying this equation:
2.74 = A * 46354.09 + 116.3
Subtracting 116.3 from both sides, we have:
-113.56 = A * 46354.09
Dividing both sides by 46354.09:
A ≈ -0.0024465
Therefore, the correct equation should be:
y = -0.0024465(x-215.3)^2 + 116.3
This equation represents the parabolic path of the baseball, where the vertex is located at (215.3, 116.3) and the coefficient A is negative to give the desired "hill" shape.