Example 1 : Find the equation of the parabola if the vertex is (4, 1) and the focus is (4, − 3) Solution : From the given information the parabola is symmetric about y … Step 3 : By applying these values in the standard form we will get the equation of the required parabola. Distance between vertex and focus = a. There are two form of Parabola Equation Standard Form and Vertex Form. You will also need to work the other way, going from the properties of the parabola to its equation. A parabola is a curve where any point is at an equal distance from a fixed point (called the focus), and a fixed straight line (called the directrix). Finding the focus of a parabola given its equation If you have the equation of a parabola in vertex form y = a ( x − h ) 2 + k , then the vertex is at ( h , k ) and the focus is ( h , k + 1 4 a ) . Standard Form: y = ax2 + bx + c. Vertex Form: y = a (x - h)2 + k. The Vertex of the Parabola:

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