Question

Find the equation of the parabola that has the following x-intercepts (-3,0) and (4,0) and passes through the point (-2,-6).

a) y = 0.25(x + 3)(x - 4)
b) y = 0.5(x + 3)(x - 4)
c) y = (x + 3)(x - 4)
d) y = -1(x + 3)(x - 4)

Answer 1

The equation of the parabola with x-intercepts (-3,0) and (4,0) that passes through (-2,-6) is found using the factored form of the quadratic equation. By substituting the given point into this form, we determine the value of 'a', resulting in the correct equation y = (x + 3)(x - 4), which corresponds to option c).

Step-by-step explanation:

Finding the Equation of a Parabola with Given Intercepts and a Point:

To find the equation of a parabola with x-intercepts (-3,0) and (4,0) that also passes through the point (-2,-6), we can use the factored form of a quadratic equation, which is y = a(x - r)(x - s), where r and s are the roots of the equation.

Given the x-intercepts, the quadratic can be written as y = a(x + 3)(x - 4). To find the value of a, we substitute the coordinates of the point (-2,-6) into the equation:

-6 = a(-2 + 3)(-2 - 4)

-6 = a(1)(-6)

To solve for a, divide both sides by -6:

a = -6 / -6 = 1

Thus, the equation of the parabola is y = (x + 3)(x - 4). Therefore, the correct answer is option c) y = (x + 3)(x - 4).