Answer: y = (1/4)x^2 + 1
Step-by-step explanation:
The equation of a parabola in vertex form is given by:
y = a(x-h)^2 + k
Where (h,k) is the vertex of the parabola and "a" is a coefficient that determines the shape of the parabola.
In this case, the vertex is given as (0,1), so h=0 and k=1. Also, the parabola passes through the point (8,17), which means that when x=8, y=17. We can use this information to solve for "a".
Substituting the values of h, k, x, and y in the equation, we get:
17 = a(8-0)^2 + 1
Simplifying this equation, we get:
17 - 1 = 64a
16 = 64a
a = 16/64
a = 1/4
Now that we know the value of "a", we can substitute it in the vertex form equation to get the final equation of the parabola:
y = (1/4)(x-0)^2 + 1
Simplifying this equation, we get:
y = (1/4)x^2 + 1
Therefore, the equation of the parabola in vertex form is y = (1/4)x^2 + 1.
Step-by-step explanation:
We start with the general equation of a parabola in vertex form and substitute the given values of the vertex and the point that the parabola passes through. Then, we solve for the coefficient "a" by simplifying the resulting equation. Once we have the value of "a", we substitute it in the vertex form equation to obtain the final equation of the parabola.