3.2-1 Vertex Form of Quadratics
• Recall…
• A quadratic equation is an equation/function
of the form f(x) = ax2 + 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) = x2
• If |a| < 1, the parabola is wider than f(x) = x2
• 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)2 + 4
• 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) = 2x2 + 4x + 3
• Ex. Graph the function k(x) = 2x2 – 4x
• Assignment
• Pg. 216
• 17-29 odd, 48, 50, 54