Question

What is the equation of a parabola that opens down and has the following x-intercepts (1,0) and (7,0)?

a) y = -(x-1)(x-7)
b) y = (x-1)(x-7)
c) y = -(x+1)(x-7)
d) y = (x+1)(x-7)

Answer 1

The equation of the parabola that opens down and has x-intercepts (1,0) and (7,0) is y = -(x-1)(x-7).

Step-by-step explanation:

The equation of a parabola that opens down and has x-intercepts (1,0) and (7,0) can be written in the form y = ax^2 + bx + c. Since the parabola opens down, the coefficient a is negative. We can determine the values of a, b, and c by plugging in the x and y coordinates of the intercepts in the equation.

For (1,0), we have 0 = a(1)^2 + b(1) + c, which simplifies to a + b + c = 0.

For (7,0), we have 0 = a(7)^2 + b(7) + c, which simplifies to 49a + 7b + c = 0.

Substituting the values from these two equations, we can solve for a, b, and c. The correct equation of the parabola is y = -(x-1)(x-7).