Write the equation for the parabola that has x− intercepts (−2,0) and (1.2,0) and y− intercept (0,−4).
y = k(x-p)(x-q) is zero at x = p and at x = q, therefore p=-2 and q = 1.2
so
y =k (x+2)(x-1.2) = k (x^2 + .8 x - 2.4)
when x = 0, y = -4
-4 = -2.4 k
k = 1 2/3 = 5/3
y = (5/3) (x^2 + .8 x - 2.4)
To write the equation for a parabola, we can start by using the factored form of a quadratic equation.
The factored form of a quadratic equation with x-intercepts (a, 0) and (b, 0) is:
(x - a)(x - b) = 0
Given the x-intercepts (-2, 0) and (1.2, 0), we can write the factored form of the equation as:
(x - (-2))(x - 1.2) = 0
Expanding this equation, we get:
(x + 2)(x - 1.2) = 0
To find the y-intercept, we substitute x = 0 into the equation. Given that the y-intercept is (0, -4), we have:
(0 + 2)(0 - 1.2) = 0
Simplifying the equation further:
2(-1.2) = 0
Multiplying:
-2.4 = 0
Since -2.4 does not equal 0, our equation is incorrect.
This implies that there might have been an error while stating the y-intercept. Please recheck the y-intercept values and provide the correct information.