What is the equation of the parabola with vertex (3, -20) and that passes through the points (7, 12)
since we know the vertex is (3,-20)
we can start with
y = a(x-3)^2 - 20
plug in the other point (7,12)
12 = a(4)^2 - 20
32 = 16a
a=2
y = 2(x-3)^2 - 20
To find the equation of a parabola, we need to determine the values of the coefficients in the general equation of a parabola:
y = a(x - h)^2 + k
where (h, k) represents the vertex of the parabola and (x, y) represents any point on the curve.
Given the information that the vertex is (3, -20), we have:
h = 3
k = -20
Next, we substitute the coordinates of the other point (7, 12) into the equation and solve for the coefficient 'a':
12 = a(7 - 3)^2 - 20
Simplifying:
12 = a(4)^2 - 20
12 = 16a - 20
16a = 32
a = 2
Finally, we substitute the values of 'a', 'h', and 'k' into the general equation to find the equation of the parabola:
y = 2(x - 3)^2 - 20
Therefore, the equation of the parabola is y = 2(x - 3)^2 - 20.
To find the equation of a parabola, you can use the standard form equation: y = a(x-h)^2 + k, where (h, k) represents the vertex of the parabola.
We are given the vertex as (3, -20), so we can substitute these values into the equation: y = a(x-3)^2 - 20.
Now, to determine the value of 'a' in the equation, we need to use the fact that the parabola passes through the point (7, 12). Substituting these values into the equation, we get:
12 = a(7-3)^2 - 20.
Now, let's solve for 'a':
12 = a(4)^2 - 20
12 = 16a - 20
32 = 16a
a = 2.
Substituting 'a' back into the equation, we have:
y = 2(x-3)^2 - 20.
Therefore, the equation of the parabola with vertex (3, -20) and passing through the point (7, 12) is y = 2(x-3)^2 - 20.