Find the x-coordinate of the vertex of a parabola that passes through the points (0,6) and (8,6)
it is half way between 0 and 8.
To find the x-coordinate of the vertex of a parabola, you can use the vertex form of a quadratic equation: y = a(x-h)^2 + k, where (h, k) represents the coordinates of the vertex.
In this case, we are given that the parabola passes through the points (0,6) and (8,6). Let's start by substituting the coordinates (0,6) into the equation:
6 = a(0 - h)^2 + k
Simplifying this equation, we get:
6 = ah^2 + k ----(Equation 1)
Next, substitute the coordinates (8,6) into the equation:
6 = a(8 - h)^2 + k
Simplifying this equation, we get:
6 = a(64 - 16h + h^2) + k
6 = 64a - 16ah + ah^2 + k
6 = ah^2 - 16ah + 64a + k ----(Equation 2)
Now, we have two equations (Equation 1 and Equation 2) with two unknowns (a and k). To solve for these unknowns, we can subtract Equation 1 from Equation 2:
(ah^2 - 16ah + 64a + k) - (ah^2 + k) = 0
64a - 16ah = 0
a(64 - 16h) = 0
Since a cannot be zero (as it will make the equation trivial), we have:
64 - 16h = 0
16h = 64
h = 64/16
h = 4
Now that we have the value of h, which represents the x-coordinate of the vertex, the answer is x = 4.