In Exercises 97–98, write the equation of each parabola in vertex form. Vertex: (-3,-1) The graph passes through the point (-2,-3).

Key Concepts

Vertex Form of a Parabola

The vertex form of a parabola is expressed as y = a(x - h)² + k, where (h, k) is the vertex of the parabola. This form is particularly useful for graphing and understanding the transformations of the parabola, as it clearly indicates the vertex's position and the direction and width of the parabola based on the value of 'a'.

Finding 'a' in Vertex Form

To determine the value of 'a' in the vertex form equation, you can substitute a known point on the parabola into the equation. In this case, using the point (-2, -3) along with the vertex (-3, -1) allows you to solve for 'a', which indicates how 'steep' or 'wide' the parabola is.

Substituting Points into Equations

Substituting points into equations is a fundamental algebraic technique used to find unknown values. By plugging in the x and y coordinates of a point into the equation, you can create an equation that can be solved for the unknown variable, which is essential for determining parameters like 'a' in the vertex form of a parabola.