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Very confused parabola
- Thread starter Jessica
- Start date
The problem states (in different words) that if x is -2 then y is zero, if x is -4 then y is zero and the vertex (highest or lowest point) is when x is -1 and y is -5.I have a HW assignment that asked what is the yintercept if the x intercepts are x=-2 and x=-4 and the vertex is (-3,-5) PLEASE HELP!!!!
So, you can solve the problem in various ways. One way is to note that the following equation solves the x intercepts as given
y = a (x - x1) (x - x2)
where x1 and x2 are the x intercepts. You need to find a so that (-3, -5) is the vertex.
Another way is to find a so that
y = a (x - h)2 + k
where the vertex is at (h, k) and has the x intercepts as given.
Or another is to solve the more involved problem of finding the values of a, b, and c so that
y = a x2 + b x + c
which satisfy the given conditions.
If that doesn't provide enough to get started let us know and show what you have done so we can help where you are stuck.
I have a HW assignment that asked what is the yintercept if the x intercepts are x=-2 and x=-4 and the vertex is (-3,-5) PLEASE HELP!!!!
x = -2 corresponds to (x + 2) = 0.
x = -4 corresponds to (x + 4) = 0.
The equation of the parabola is y = a(x + 2)(x + 4).
Using the vertex, substitute -5 for y and -3 for each x. Solve for a.
Then, to find the y-intercept, let x = 0 in the completed equation.