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. • 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 = –(x – 50)2 + 150 y = – Image with alt text: 3 over 50 ( x – 50) 2 + 150 y = –(x – 150)2 + 50 y = – Image with alt text: 3 over 2 ( x – 150) 2 + 50 y = –(x – 100)2 + 150 y = – Image with alt text: 3 over 20 ( x – 100) 2 + 150 y = –(x – 50)2 + 150
The correct equation in vertex form that represents the path of the ball is: y = -(x - 50)^2 + 150
To find the equation in vertex form that represents the path of the golf ball, we need to determine the vertex coordinates of the parabolic curve.
Given the points (0, 0), (50, 150), and (100, 0), we can determine that the vertex of the parabola lies at the point (50, 150).
So, the equation in vertex form is:
y = a(x - h)^2 + k
where (h, k) represents the vertex coordinates. Substituting the values (50, 150) into the equation, we obtain:
y = a(x - 50)^2 + 150
To find the value of the coefficient 'a', we can use one of the other points on the graph (0, 0). Substituting the values (0, 0) into the equation, we can solve for 'a':
0 = a(0 - 50)^2 + 150
0 = 2500a + 150
2500a = -150
a = -150/2500
a = -3/50
Therefore, the equation in vertex form that represents the path of the golf ball is:
y = -3/50(x - 50)^2 + 150
So, the correct answer is: y = -3/50(x - 50)^2 + 150
To find the equation in vertex form that represents the path of the golf ball, we need to determine the vertex (h, k) of the parabola.
From the given information, we can identify the points (0, 0), (50, 150), and (100, 0). The vertex lies on the axis of symmetry, which is halfway between the x-coordinate values of the given points. In this case, the axis of symmetry is x = 50.
To find the y-coordinate of the vertex, substitute x = 50 into the equation and solve for y:
y = -(x - 50)^2 + 150
y = -(50 - 50)^2 + 150
y = -0^2 + 150
y = 150
Therefore, the vertex of the parabola is (50, 150).
The equation of a parabola in vertex form is y = a(x - h)^2 + k, where (h, k) represents the vertex and "a" determines the shape and direction of the parabola.
Using the vertex (50, 150), we have:
y = a(x - 50)^2 + 150
To determine the value of "a," we can use one of the given points. Let's use (0, 0):
0 = a(0 - 50)^2 + 150
0 = 2500a + 150
-150 = 2500a
a = -150 / 2500
a = -3/50
Substituting this value of "a" into the equation, we get:
y = -(3/50)(x - 50)^2 + 150
Therefore, the equation in vertex form that represents the path of the golf ball is:
y = -(3/50)(x - 50)^2 + 150
Therefore, the correct response is:
y = -(3/50)(x - 50)^2 + 150