Question

Find the equation of the parabola given the information below. x-intercepts of 1 and -2 and going through the point (0, 5).

A) y = -x^2 + 3x + 2
B) y = x^2 + 3x + 2
C) y = -x^2 - 3x + 2
D) y = x^2 - 3x + 2

Answer 1

The equation of the parabola is y = x^2 + 3x + 5.

Step-by-step explanation:

The equation of a parabola can be written in the form y = ax^2 + bx + c, where a, b, and c are constants. To find the equation of the parabola given the x-intercepts of 1 and -2 and going through the point (0, 5), we need to substitute the x-intercepts and the point into the equation and solve for a, b, and c.

Substituting the x-intercepts, we have:

0 = a(1)^2 + b(1) + c (equation 1)

0 = a(-2)^2 + b(-2) + c (equation 2)

Substituting the point (0, 5), we have:

5 = a(0)^2 + b(0) + c

Simplifying equation 3, we get:

5 = c

Substituting this value of c into equations 1 and 2, we can solve for a and b. By solving the system of equations, we find a = 1 and b = 3.

Therefore, the equation of the parabola is y = x^2 + 3x + 5, which corresponds to option B.