Vertex Form Quadratics

The vertex form of a quadratic equation is f(x) = a(x-h)² + k, where (h, k) is the vertex of the parabola.

A parabola opens up if the coefficient 'a' in the vertex form f(x) = a(x-h)² + k is positive, and it opens down if 'a' is negative.

The axis of symmetry is a vertical line that passes through the vertex of the parabola, dividing it into two mirror-image halves.

The equation of the axis of symmetry is x = h.

The vertex represents the highest or lowest point of the parabola, depending on whether it opens up or down.

To find the vertex from the standard form ax² + bx + c, use the formula h = -b/(2a) and then substitute h back into the equation to find k.

The x-intercepts are the points where the parabola crosses the x-axis, found by setting f(x) = 0 and solving for x.

The 'a' value determines the width and direction of the parabola; larger absolute values of 'a' make the parabola narrower.

The y-intercept is the point where the parabola crosses the y-axis, which can be found by evaluating f(0) in the vertex form.

To graph a quadratic function in vertex form, plot the vertex, draw the axis of symmetry, and then plot additional points on either side of the vertex.