Write+the+Equation+of+the+Parabola

Write the Equation

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

**__Writing the Equation of a Parabola__** Notice that the vertex of the parabola is located at (3, 1). Also note that the point (2, 3) is on the graph.

Vertex=(h,k)

//y// = //a//(//x// – //h//)^2 + //k// || //y// = //a//(//x// – 3)^2 + 1 || 3 = //a//(2 – 3)^2 + 1 || 3 = //a// + 1 || //a// = 2 || //y// = 2(//x// – 3)^2 + 1 ||
 * Use vertex form || 
 * Substitute //h// = 3 and //k// = 1 || 
 * Substitute //x// = 2 and //y// = 3 || 
 * Simplify || 
 * Solve for //a// || 
 * //The equation of the parabola is// || 

Connections:

Writting the equation relates to graphing the parabola because you have to be able to understand how to read the equation to graph it. Standard and Vertex are two diffrent ways to write an equation of a parabola. You can write an equation of a parabola in eaither standard (y=ax^2+bx+c) or in vertex form (y=a(x-h)^2+K).