3.2-1 Vertex Form of Quadratics

1. 3.2-1 Vertex Form of Quadratics

2. Recall… • A quadratic equation is an equation/function of the form f(x) = ax2 + bx + c

3. 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)

4. 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

5. 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

6. 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!

7. Ex. Graph the parabola of the function h(x) = -(x + 1)2 + 4 • Vertex? • X-intercepts?

8. 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

9. Ex. Graph the function J(x) = 2x2 + 4x + 3

10. Ex. Graph the function k(x) = 2x2 – 4x

11. Assignment • Pg. 216 • 17-29 odd, 48, 50, 54