Determine the equation of a parabola with vertex (7, -2), and passing through the point (6, 0). Graph the parabola.
Since you have the vertex, use that for the equation.
y = a(x-7)^2 - 2
Now just plug in your other point to find a.
To determine the equation of a parabola with a given vertex and passing through a point, we can use the standard form of a parabola equation:
y = a(x - h)^2 + k
where (h, k) represents the vertex coordinates.
Given that the vertex is (7, -2), we substitute these values into the equation:
y = a(x - 7)^2 - 2
The parabola passes through the point (6, 0), which means when we substitute these values into the equation, the equation becomes true:
0 = a(6 - 7)^2 - 2
Simplifying the equation, we have:
0 = a(-1)^2 - 2
0 = a - 2
Adding 2 to both sides, we get:
2 = a
Therefore, the value of 'a' is 2.
Substituting the value of 'a' into the equation, we have:
y = 2(x - 7)^2 - 2
This is the equation of the parabola with the given vertex and passing through the point.
To graph the parabola, we can plot the vertex at (7, -2) and then use additional points to plot the shape of the parabola.
Using the equation, we can substitute different values of 'x' to obtain the corresponding 'y' values. For example, when we substitute x = 6 into the equation, we get y = 0.
Similarly, we can substitute x = 8 to get y = 0, and x = 5 to get y = -4.
Plotting these points on a coordinate plane and connecting them, we can graph the parabola.