find the x-coordinate if the vertex of a parabola that passes through the points (0,3) and (7.15,3). Round approximate results to the second decimal place.
would I do 0+7.15/2 to get the x-coordinate?
Yes that's how to do it, you find the midpoint.
To find the x-coordinate of the vertex of a parabola, you can use the formula:
x = (-b) / (2a)
In this case, the coordinates of the two given points are (0, 3) and (7.15, 3). Since the y-coordinates are the same, the vertex of the parabola must lie on the line y = 3.
We can set up an equation using the general form of a parabola:
y = ax^2 + bx + c
Using the fact that the vertex lies on the line y = 3, we substitute y with 3 and get:
3 = ax^2 + bx + c
Since the y-intercept is 3, the equation becomes:
0 = ax^2 + bx + 3
Now let's substitute the first set of coordinates (0, 3) into this equation:
0 = a(0)^2 + b(0) + 3
Simplifying this equation, we get:
0 = 3
This tells us that a = 0. Now substitute the second set of coordinates (7.15, 3) into the equation:
0 = a(7.15)^2 + b(7.15) + 3
Simplifying further, we have:
50.9225a + 7.15b + 3 = 0
Since a = 0, we can simplify this equation to:
7.15b + 3 = 0
Solving for b, we find:
b = -3 / 7.15
b ≈ -0.42
Now that we have the values of a and b, we can find the x-coordinate of the vertex using the formula:
x = (-b) / (2a)
Substituting the values, we get:
x = (-(-0.42)) / (2 * 0)
x = 0 / 0
However, the denominator is zero in this case, which means the parabola does not have a vertical line of symmetry and there is no vertex or x-coordinate to find.
To find the x-coordinate of the vertex of a parabola, you can use the formula:
x = (-b) / (2a)
In this case, we need to find the value of x when the parabola passes through the points (0,3) and (7.15,3).
First, let's find the equation of the parabola.
Since the parabola passes through the vertex and the vertex lies on the axis of symmetry, we can conclude that the x-coordinate of the vertex is the midpoint of the x-coordinates of the given points.
To find the x-coordinate of the vertex, we can use the formula:
x_vertex = (x1 + x2) / 2
where (x1, y1) = (0,3) and (x2, y2) = (7.15,3).
x_vertex = (0 + 7.15) / 2
x_vertex = 7.15 / 2
x_vertex = 3.575
So, the x-coordinate of the vertex is approximately 3.58 (rounded to the second decimal place).