what is the intercept form of this parabola with intercepts at: x = -2, x = 3, and y = -4
start with y=(x+2)(x-3)
at x=0, y=-6
but you want y(0)=-4
so,
y = (2/3)(x+2)(x-3)
multiplying by 2/3 does not change the roots, but it does shift the y-intercept.
To find the intercept form of a parabola, we need to determine the equation in the form y = a(x - h)(x - k), where (h, k) represents the coordinates of the vertex.
Given that the parabola has x-intercepts at x = -2 and x = 3, we know that the factors of the equation are (x + 2) and (x - 3).
Now, let's find the y-intercept. The y-intercept occurs when x = 0, so we substitute this value into our equation to get:
y = a(0 + 2)(0 - 3)
= a(-2)(-3)
= 6a
Since y = -4 at the y-intercept, we can equate this to 6a and solve for 'a':
-4 = 6a
Dividing both sides by 6, we find:
a = -4/6
= -2/3
Now that we have 'a', we can substitute it and the factors into our equation:
y = (-2/3)(x + 2)(x - 3)
Thus, the intercept form of the given parabola is y = (-2/3)(x + 2)(x - 3).