has a vertex of (0,2) and points (1,8)find a,b,c
To find the equation of a parabola, given a vertex and another point, we can use the general form of the equation for a parabola: y = ax^2 + bx + c.
Given that the vertex of the parabola is (0,2), we know that the x-coordinate of the vertex (h) is 0, and the y-coordinate of the vertex (k) is 2.
So, substitute the values of h and k into the equation: y = a(x - h)^2 + k
Substituting (0,2), we get: y = a(x - 0)^2 + 2
Simplifying further, we get: y = ax^2 + 2
Now, we need to find the value of 'a'. For that, we can use the other given point on the parabola, which is (1,8).
Substituting the values of x and y from the second point into the equation, we get: 8 = a(1)^2 + 2
Calculating further, we have: 8 = a + 2
Subtracting 2 from both sides, we get: 6 = a
Therefore, the value of 'a' is 6.
Now, we can rewrite the equation of the parabola with the value of 'a' as: y = 6x^2 + 2x + c.
However, we still need to find the values of 'b' and 'c'. To find them, we need one more point on the parabola. If there are no additional points provided, we cannot determine the precise values of 'b' and 'c'.