Find an equation of the parabola that has the indicated vertex and whose graph passes through the given point
Vertex:2,-1 Point:4,-3
given the vertex, you know that
y = a(x-2)^2 - 1
Now plug in the point to find a:
a(4-2)^2 - 1 = -3
To find the equation of a parabola given the vertex and a point on the graph, we can use the standard form equation of a parabola:
y = a(x - h)² + k
where (h, k) represents the vertex of the parabola.
We are given that the vertex is (2, -1) and a point on the graph is (4, -3).
1. Substitute the vertex coordinates into the equation:
y = a(x - 2)² - 1
2. Substitute the coordinates of the given point into the equation to find the value of 'a':
-3 = a(4 - 2)² - 1
-3 = a(2)² - 1
-3 = 4a - 1
3. Solve for 'a':
4a = -2
a = -2/4
a = -1/2
4. Substitute the value of 'a' back into the equation:
y = (-1/2)(x - 2)² - 1
Therefore, the equation of the parabola with a vertex of (2, -1) and passing through the point (4, -3) is:
y = (-1/2)(x - 2)² - 1