Graph quadratic functions in vertex form (Tutorial Only)

Learning Objectives Identify the vertex (h, k) and the value of 'a' from a quadratic equation in vertex form. Determine the axis of symmetry for a parabola from its vertex form equation. Predict whether a parabola opens upwards or downwards based on the sign of the 'a' value. Calculate the y-intercept of a quadratic function given in vertex form. Find at least two additional points on a parabola using the axis of symmetry. Accurately sketch the graph of a quadratic function using the vertex, y-intercept, and symmetric points. Ever wonder about the perfect arc of a water fountain or a basketball shot? 🏀 That path is a parabola, and vertex form is the secret code to graphing it instantly! This tutorial will teach you how to graph quadratic functions using...

TermDefinitionExample ParabolaThe symmetrical, U-shaped curve that is the graph of a quadratic function.The path a ball takes when you throw it into the air. Vertex FormA specific format for a quadratic equation, y = a(x - h)^2 + k, which reveals the vertex and other properties of the parabola.The equation y = 2(x - 3)^2 + 4 is in vertex form. VertexThe highest or lowest point on a parabola. It is the turning point of the curve.For the parabola y = (x - 2)^2 + 1, the vertex is at the point (2, 1). Axis of SymmetryThe vertical line that passes through the vertex and divides the parabola into two perfect mirror images.For a parabola with a vertex at (2, 1), the axis of symmetry is the vertical line x = 2. Direction of OpeningDescribes whether the parabola opens upwards (like a cup) or downw...

Vertex Form of a Quadratic Function y = a(x - h)^2 + k This is the standard vertex form. The parameter 'a' controls the direction of opening and the vertical stretch/compression. The point (h, k) is the vertex of the parabola. Vertex Coordinates Vertex = (h, k) The coordinates of the vertex are directly taken from the vertex form equation. Be careful with the sign of 'h'; the form is (x - h), so if you see (x + 3), it means (x - (-3)), and h = -3. Axis of Symmetry x = h The axis of symmetry is always a vertical line that passes through the x-coordinate of the vertex. Its equation is simply x = h.