When a parabola opens left or right, its equation in the standard form is of the form x = ay 2 + by + c. Step - 4: Write the vertex (h, k) as an ordered pair.Step - 3: To find the y-coordinate (k) of the vertex, substitute x = h in the expression ax 2+ bx + c.Step - 2: Find the x-coordinate of the vertex using the formula, h = -b/2a.Step - 1: Compare the equation of the parabola with the standard form y = ax 2 + bx + c.īy comparing y = 2x 2 - 4x + 1 with the above equation, a = 2, b = -4, and c = 1.The steps are explained with an example where we will find the vertex of the parabola y = 2x 2 - 4x + 1. Here are the steps to find the vertex (h, k) of such parabolas. When a parabola opens up or down, its equation in the standard form is of the form y = ax 2 + bx + c. Let us see the steps to find the vertex of the parabola in each case. We know that the equation of a parabola in standard form can be either of the form y = ax 2 + bx + c (up/down) or of the form x = ay 2 + by + c (left/right). In each of the cases, the parabola opens up if a > 0, and it opens down if a 0, and it opens to the left side if a < 0.įinding Vertex of a Parabola From Standard Form The equation of a top/bottom opened parabola can be in one of the following three forms: The equation of any parabola involves a quadratic polynomial. There can be two types of equations of a parabola which represent 4 different types of parabolas. The vertex of a parabola is also the point of intersection of the parabola and its axis of symmetry. A parabolic function has either a maximum value (if it is of the shape '∩') or a minimum value (if it is of the shape 'U"). The vertex of a parabola is a point at which the parabola makes its sharpest turn.
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