The graph below models the path of a golf ball after it was hit. Write an equation in vertex form that represents the path of the ball.
graph showing path of golf ball• The x-axis is between 0 and 100 and in increments of 20.
• The y-axis is between 0 and 150 and in increments of 30.
• The curve connects the points left-parenthesis 0 comma 0 right-parenthesis, left-parenthesis 50 comma 150 right-parenthesis, and left-parenthesis 100 comma 0 right-parenthesis.
(1 point)
Responses
y = –3 over 50(x – 50)2 + 150
y = – Image with alt text: 3 over 50 ( x – 50) 2 + 150
y = –3 over 2(x – 150)2 + 50
y = – Image with alt text: 3 over 2 ( x – 150) 2 + 50
y = –3 over 20(x – 100)2 + 150
y = – Image with alt text: 3 over 20 ( x – 100) 2 + 150
y = –50 over 30(x – 50)2 + 150
The correct equation in vertex form that represents the path of the golf ball is:
y = -3/50(x - 50)^2 + 150
The correct equation in vertex form that represents the path of the golf ball is:
y = -3/50(x - 50)² + 150
To write an equation in vertex form that represents the path of the golf ball, we need to identify the vertex of the parabolic curve formed by the path. The vertex is the highest or lowest point of the curve.
From the given information, we can see that the points (0,0), (50,150), and (100,0) are on the curve. The vertex lies on the line of symmetry which passes through the midpoint of the x-coordinates of the two points on either side of the vertex.
The midpoint of (0,0) and (50,150) is ((0+50)/2, (0+150)/2) = (25, 75).
Therefore, the vertex of the parabolic curve is (25, 75).
The general vertex form of a parabola is given by:
y = a(x - h)^2 + k
Where (h, k) represents the vertex of the parabola.
Substituting the values of the vertex (25, 75) into the equation, we get:
y = a(x - 25)^2 + 75
Now, we need to find the value of a. We can do this by substituting one of the given points on the curve, such as (50, 150), into the equation and solving for a.
150 = a(50 - 25)^2 + 75
150 = a(25)^2 + 75
150 - 75 = 625a
75 = 625a
a = 75/625
Simplifying further:
a = 3/25
Therefore, the equation in vertex form that represents the path of the golf ball is:
y = (3/25)(x - 25)^2 + 75
Simplifying:
y = (3/25)(x^2 - 50x + 625) + 75
y = (3/25)x^2 - (6/5)x + 93
So, the correct equation in vertex form is:
y = (3/25)x^2 - (6/5)x + 93