Vertex Form Quadratics

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

Changing 'a' from 1 to -¾ makes the graph wider and opens it downward.

The vertex is (-4, -3).

This represents a translation of the parent function $$y = x^2$$ to the right by 5 units and up by 2 units.

A negative 'a' value reflects the graph over the x-axis.

The axis of symmetry can be found using the formula $$x = h$$ , where (h, k) is the vertex.

The term 'k' represents the vertical shift of the graph. It indicates how far the graph is translated up or down.

The maximum value of the function is 4, which occurs at the vertex.

The parent function of a quadratic equation is $$y = x^2$$ .