Suppose a parabola has its vertex at (0, 1) and its zeros at x = -3 and x = 3. Then equals _____.
A. 9-x^2
B. 1-1/9x^2
C. x^2-1
D. x^2-9
vertex at (0,1) means y = -ax^2 + 1 where a>0.
since y=0 when x=3, we have
y = -1/9 x^2 + 1
(B)
B. Y = 1-(1/9)x^2 = 1 - x^2/9.
V(0,1).
When Xv = 0,
Y = 1-0/9 = 1.
When X = -3,
Y = 1 - (-3)^2 / 9 = 1--1 = o.
When X = 3,
Y = 1- 3^2 / 9 = 1 - 1 = 0.
Choice B satisfies all requirements.
Therefore,the answer is B.
To find the equation of the parabola, we can start by using the vertex form of the equation of a parabola:
y = a(x - h)^2 + k
Where (h, k) represents the vertex of the parabola.
Given that the vertex is (0, 1), we can substitute these values into the equation:
y = a(x - 0)^2 + 1
Simplifying this equation, we get:
y = ax^2 + 1
Next, we need to find the value of the coefficient 'a'. The zeros of the parabola are the values of x where the graph crosses the x-axis. In this case, the zeros are x = -3 and x = 3.
To find the zeros, we can set y equal to zero and solve for x:
0 = ax^2 + 1
Substituting in the value of x = -3, we get:
0 = a(-3)^2 + 1
0 = 9a + 1
Solving for 'a', we find:
-9a = 1
a = -1/9
Now that we know the value of 'a', we can substitute it back into the equation for y:
y = (-1/9)x^2 + 1
Comparing this form with the given answer choices, we can see that the correct answer is:
B. 1 - (1/9)x^2