Quadratics - Vertex Form

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

The 'a' value determines the direction of the parabola (upward if a > 0, downward if a < 0) and the width of the parabola.

Changing 'h' translates the graph horizontally. If 'h' increases, the graph shifts to the right; if 'h' decreases, it shifts to the left.

Changing 'k' translates the graph vertically. If 'k' increases, the graph shifts upward; if 'k' decreases, it shifts downward.

The vertex of the function is (3, 5).

The axis of symmetry is the vertical line $$x = -2$$ .

It means the entire graph of the function is shifted 7 units downward on the y-axis.

It means the entire graph of the function is shifted 14 units to the left on the x-axis.

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

If 'a' is positive, the parabola opens upward; if 'a' is negative, it opens downward.