Find the vertix of the parabola

Learning Objectives Identify the vertex of a parabola directly from its vertex form, y = a(x - h)^2 + k. Calculate the coordinates of the vertex from the general quadratic form, y = ax^2 + bx + c, using the formula x = -b/(2a). Convert a quadratic equation from general form to vertex form by completing the square. Distinguish between vertical and horizontal parabolas and find their respective vertices. Determine whether the vertex represents a maximum or minimum point of the parabola based on its orientation. Apply the concept of the vertex to solve problems involving projectile motion and optimization. Ever wondered about the highest point a basketball reaches in a perfect shot? 🏀 That peak point is the vertex of a parabolic path! This tutorial will teach you three powerf...

TermDefinitionExample ParabolaA U-shaped curve representing a quadratic function. It is the set of all points in a plane that are equidistant from a fixed point (the focus) and a fixed line (the directrix).The graph of the equation y = x^2 is a simple parabola that opens upwards with its vertex at the origin (0, 0). VertexThe point where the parabola changes direction. It is the minimum point if the parabola opens upwards or the maximum point if it opens downwards.For the parabola y = (x - 2)^2 + 1, the vertex is at the point (2, 1). Axis of SymmetryA vertical or horizontal line that passes through the vertex and divides the parabola into two mirror-image halves.For y = x^2 + 4x + 5, the axis of symmetry is the vertical line x = -2, which passes through its vertex (-2, 1). Vertex Form (Ve...

Vertex Form Formula For a parabola in the form y = a(x - h)^2 + k, the vertex is at the point (h, k). Use this when the equation is already in vertex form. Simply identify the values of 'h' and 'k'. Be careful with the sign of 'h'. General Form Vertex Formula For a parabola in the form y = ax^2 + bx + c, the x-coordinate of the vertex is given by x = -b / (2a). Use this formula to find the x-coordinate of the vertex. To find the y-coordinate, substitute this x-value back into the original equation. Horizontal Parabola Vertex Form For a parabola in the form x = a(y - k)^2 + h, the vertex is at the point (h, k). This is for parabolas that open sideways. Notice that 'h' is the x-coordinate and 'k' is associated with the...