graph of a parabola has the following:
y-intercept at 60
minimum at (4.25, -12.25)
zero at 6
Find the other zero.
(0,60)
(60,0)
vertex along x = 4.25, axis of symmetry
vertex at (4.25,-12.25)
Sketch it.
The zero is 6-4.25 = 1.75 to the right of the axis of symmetry
Therefore the other zero is at 4.25 -1.75 = 2.5 so (2.5,0)
a1=8,d=3,n=16
the one is a little below the a
To find the other zero of the parabola, we need to use the given information and the properties of a quadratic equation.
We are given that the parabola has a y-intercept at 60, which means that when x = 0, y = 60. This gives us one point on the parabola: (0, 60).
We are also given that the minimum point is located at (4.25, -12.25). The vertex form of a parabola is given by y = a(x-h)^2 + k, where (h, k) represents the vertex. In this case, (h, k) = (4.25, -12.25).
Substituting the vertex values into the vertex form, we get the equation: y = a(x-4.25)^2 -12.25.
Now, we can use the zero(s) of the parabola to solve for the value of 'a' in the equation.
The zero(s) are the x-intercepts of the parabola, which correspond to the values of x where y = 0.
We already know one zero is at x = 6. Substituting this value into the equation, we get: 0 = a(6 - 4.25)^2 - 12.25.
Simplifying the equation, we have: 0 = a(6.5)^2 - 12.25.
Now, we can solve for 'a'. Rearranging the equation, we have: 12.25 = a(6.5)^2.
Dividing both sides of the equation by (6.5)^2, we find: a = 12.25 / (6.5)^2.
Calculating this, we have: a ≈ 0.35.
Now that we have the value of 'a', we can determine the other zero(s) of the parabola.
Substituting 'a' and the vertex values into the equation, we get: 0 = 0.35(x - 4.25)^2 - 12.25.
Now, we can solve for x when y = 0: 0 = 0.35(x - 4.25)^2 - 12.25.
Adding 12.25 to both sides of the equation gives: 12.25 = 0.35(x - 4.25)^2.
Dividing both sides of the equation by 0.35, we find: (12.25 / 0.35) = (x - 4.25)^2.
Taking the square root of both sides of the equation gives: √(12.25 / 0.35) = x - 4.25.
Now, we can solve for x by adding 4.25 to both sides of the equation: x = 4.25 ± √(12.25 / 0.35).
Calculating this, we find two possible values for x:
x ≈ 4.25 + √(12.25 / 0.35)
x ≈ 4.25 - √(12.25 / 0.35)
Therefore, the other zero(s) of the parabola are approximately the two values obtained from the above calculations.