3.2-1 Vertex Form of Quadratics

Recall… A quadratic equation is an equation/function of the form f(x) = ax 2 + bx + c

Vertex Form To facilitate an easier way to graph, we can look at the vertex form of a quadratic Vertex = highest or lowest point of a parabola (an ordered pair point) g(x) = a(x – h) 2 + k – Vertex of (h, k)

Behavior of Vertex Form The vertex form can quickly tell us some basic information of the parabola With regards to a: – If a < 0, opens downward – If a > 0, opens upwards

In addition… If |a| > 1, the parabola is more narrow than f(x) = x 2 If |a| < 1, the parabola is wider than f(x) = x 2

To graph, all we simply need is: – A) the vertex – B) the x-intercepts – C) know which way the graph points No more test points!

Ex. Graph the parabola of the function h(x) = -(x + 1) Vertex? X-intercepts?

What if the function is not in vertex form? We can rewrite a function in terms of the vertex form – What kind of polynomial is factored in the function? – CTS

Ex. Graph the function J(x) = 2x 2 + 4x + 3

Ex. Graph the function k(x) = 2x 2 – 4x

Assignment Pg odd, 48, 50, 54