Question

Write an equation for the parabola that has the given vertex and passes through the given point.

Vertex: (-1, -3)
Point: (1, 5)

A) f(x) = -2(x + 1)2 - 3
B) f(x) = 2(x + 1)2 - 3
C) f(x) = -2(x - 1)2 - 3
D) f(x) = 2(x - 1)2 - 3

Answer 1

The correct equation of the parabola with vertex (-1, -3) that passes through the point (1, 5) is found by using the vertex form and calculating the coefficient 'a'. The resulting parabola is represented by the equation f(x) = 2(x + 1)^2 - 3, which corresponds to option B.

Step-by-step explanation:

To determine the equation of a parabola given a vertex and a point it passes through, we use the vertex form of a quadratic equation, which is y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola. We know that the vertex is (-1, -3) and that the parabola passes through the point (1, 5). Substituting these values, we find:

y = a(x + 1)^2 - 3

Now, plug in the point (1, 5) to find a:

5 = a(1 + 1)^2 - 3

5 = a(2)^2 - 3 → 5 = 4a - 3

8 = 4a

a = 2

Now we can write the full equation of the parabola as:

y = 2(x + 1)^2 - 3

Therefore, the correct option is B) f(x) = 2(x + 1)^2 - 3.