Question

The minimum of a parabola is located at (–1, –3). The point (0, 1) is also on the graph. Which equation can be solved to determine the a value in the function representing the parabola?1 = a(0 + 1)^2 – 31 = a(0 – 1)^2 + 30 = a(1 + 1)^2 – 30 = a(1 – 1)^2 + 3

Answer 1

Given:

The minimum of a parabola is located at (–1, –3).

The general equation of the parabola will be as follows:

`y=a(x-h)^2+k`

Where (h,k) is the vertex of the parabola

given the vertex is the minimum point (-1, -3)

So, h = -1, k = -3

substitute into the general form, so, the equation of the parabola will be:

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

The point (0, 1) is also on the graph.

So, when x = 0, y = 1

substitute with the given point to determine the value of (a)

So, the equation will be:

`1=a(0+1)^2-3`

So, the answer will be the first option:

1 = a(0 + 1)^2 – 3