Question

Write an equation in intercept form of the parabola that passes through the point (3,40) and has x-intercepts −5 and 4.

Answer 1

The equation of the parabola with x-intercepts at −5 and 4, and passing through the point (3, 40), is y = −5(x + 5)(x - 4).

Step-by-step explanation:

To write the equation of a parabola in intercept form, we need the x-intercepts and one additional point. Since the x-intercepts are given as −5 and 4, we can write the parabola in its intercept form as:

y = a(x + 5)(x - 4)

To find the value of 'a', we use the point (3, 40) which lies on the parabola:

40 = a(3 + 5)(3 - 4)

40 = a(8)(-1)

a = −5

So, the equation of the parabola is:

y = −5(x + 5)(x - 4)

Answer 2

The equation of this parabola will have the form f(x) = a(x+5)(x-4), which works out to f(x) = a(x^2 + x - 20). Since the parabola passes thru (3,40),

40 = a(3^2 + 3 - 20), or 40 = a(-8), so a = -5.

Thus, the equation of this parabola is y = -5(x^2 + x - 20).