# A.6.15.2 A Whole New Form

- Author:
- Katie Akesson

Here are two sets of equations for quadratic functions. In each column, the expressions that define the output are equivalent. f(x) = g(x) = h(x) and p(x) = q(x) = r(x) You may recognize 2 of the forms; the first row is standard form and the second row is factored form. The third row is a new form for today! The expression that defines h is written in vertex form. We can show that it is equivalent to the expression defining by expanding the expression: Show that the expressions defining p(x), q(x), and r(x) are equivalent by multiplying out r(x).

Here are graphs representing the quadratic functions, they are written in ** vertex** form.
Vertex form contains the vertex (the point on the parabola that lies on the line of symmetry of the parabola - or what you can think of as the "middle" point).
Notice the

**x-value**is subtracted from x in the equation, so it has the opposite sign of the vertex. The y-value of the vertex has the same sign in the vertex point as in the equation. Vertex is the point (-2, -4) Vertex is the point (3, 4)