Find the axis of symmetry of a parabola

Learning Objectives Define the axis of symmetry and its relationship to the vertex of a parabola. Derive the equation for the axis of symmetry from a quadratic function in standard form, y = ax^2 + bx + c. Identify the equation for the axis of symmetry directly from a quadratic function in vertex form, y = a(x-h)^2 + k. Calculate the equation for the axis of symmetry from a quadratic function in factored form, y = a(x-p)(x-q). Correctly write the axis of symmetry as a vertical line equation (x = constant). Visually identify and graph the axis of symmetry for a given parabola. Ever wonder how a satellite dish focuses signals to one single point? 📡 The secret lies in its perfect parabolic symmetry! This tutorial will teach you how to find the axis of symmetry, the invisible...

TermDefinitionExample ParabolaThe characteristic U-shaped curve produced by a quadratic function (an equation of the form y = ax^2 + bx + c).The graph of y = x^2 is a simple parabola that opens upwards with its turning point at the origin (0,0). Axis of SymmetryA vertical line that passes through the vertex of a parabola, dividing it into two congruent, mirror-image halves. Its equation is always in the form x = c, where c is a constant.For the parabola y = x^2, the axis of symmetry is the y-axis, which has the equation x = 0. VertexThe highest or lowest point on a parabola, also known as the turning point. The vertex always lies on the axis of symmetry.In y = (x-3)^2 + 5, the vertex is at the point (3, 5). Standard FormA quadratic function written as y = ax^2 + bx + c, where a, b, and c...

Axis of Symmetry from Standard Form For y = ax^2 + bx + c, the axis of symmetry is the line x = -b / (2a) Use this formula when the quadratic equation is expanded. Identify the coefficients 'a' and 'b' and substitute them into the formula to find the x-value where the line of symmetry is located. Axis of Symmetry from Vertex Form For y = a(x-h)^2 + k, the axis of symmetry is the line x = h Use this when the equation is in vertex form. The axis of symmetry is simply the x-coordinate of the vertex, 'h'. Be mindful of the sign inside the parentheses. Axis of Symmetry from Factored Form For y = a(x-p)(x-q), the axis of symmetry is the line x = (p + q) / 2 Use this when the equation is factored. The axis of symmetry is located exactly halfway...