Vertex-Form

Parabola

The vertex form is given by $$y = a(x - h)^2 + k$$ , where (h, k) is the vertex of the parabola.

Complete the square to rewrite the equation in the form $$y = a(x - h)^2 + k$$ .

The 'a' value determines the direction and width of the parabola. If 'a' is positive, the parabola opens upwards; if negative, it opens downwards.

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves. It can be found using the formula $$x = h$$ , where (h, k) is the vertex.

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

For a quadratic in standard form $$y = ax^2 + bx + c$$ , the vertex can be found using the formula $$h = -\frac{b}{2a}$$ and then substituting h back into the equation to find k.

The vertex represents the maximum or minimum point of the parabola, depending on the direction it opens.

The vertex form is $$y = (x - 3)^2 + 1$$ .

The vertex is given by the point (h, k) in the vertex form $$y = a(x - h)^2 + k$$ .