Question

Given a parabola opening up or down with a vertex at (-4, 2) and passing through the point (-3, 9/4), find its equation in vertex form. Simplify any fractions.

A) y = (1/4)(x + 4)^2 + 2
B) y = (9/4)(x + 4)^2 + 2
C) y = (4/9)(x + 4)^2 + 2
D) y = (4/3)(x + 3)^2 + 9
E) y = (3/4)(x + 4)^2 + 2

Answer 1

The equation of the parabola with vertex (-4, 2) and passing through (-3, 9/4) is y = (1/4)(x + 4)^2 + 2, which is answer option A.

Step-by-step explanation:

To find the equation of a parabola in vertex form, given vertex (-4, 2) and passing through the point (-3, 9/4), we start with the general vertex form of a parabola which is y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola. Plugging in the vertex coordinates, we get y = a(x + 4)^2 + 2. Now we need to determine the value of 'a'.

To find 'a', we use the point (-3, 9/4) which lies on the parabola. Plugging in these coordinates into the equation, we have 9/4 = a(-3 + 4)^2 + 2. Solving for 'a', we calculate a = 1/4. Therefore, the equation of the parabola is y = (1/4)(x + 4)^2 + 2, which corresponds to answer option A. This equation signifies that the parabola opens upwards, as 'a' is positive.