WARM UP Use f(x) = 3x 2 + 4x – 6 to evaluate the following. 1. f(2) 2. f(-4) 3. f(0)

WARM UPUse f(x) = 3x2 + 4x – 6 to evaluate the following.1. f(2)2. f(-4)3. f(0)

Math II UNIT QUESTION: What is a quadratic function? Standard: MM2A3, MM2A4 Today’s Question: How do you graph quadratic functions in standard form? Standard: MM2A4.a.

1. Put the equation in standard form: 3. Find the axis of symmetry: (vertical line) Notes-Graphing Quadratic Equations 3.1 Steps to graph quadratic equations 2. Identify the values of a, b, and c.

Steps to graph quadratic equations (cont.) 4. Find your vertex (substitute your axis of symmetry back into the original equation and solve for y). 5. Construct a table of values for x and y. Choose values of x, two above and two below your x value in the vertex. 6. Plot the points and connect them with a U-shaped curve.

If a is positive, then the parabola will open up. If a is negative, then the parabola will open down. Graph opens up or opens down?

OPENS DOWN a = -1 b = 2 c = -1 

Tell whether the graph opens up or down. Graph each using a T-chart. Find the axis of symmetry &  vertex . Use a dotted line to graph the axis of symmetry. OPENS UP a = 1 b = -6 c = 5 

OPENS DOWN a = -1 b = -2 c = 3 

OPENS DOWN a = 1 b = 2 c = -6 

OPENS UP a = 1 b = 8 c = 13 

Converting to Vertex Form from Standard Form • Find the vertex point, (h, k): • a will be the a from the standard form equation. • 3. Substitute into y = a (x-h)2 + k

Converting to Vertex Form from Standard Form • Convert y = 2x2 – 4x + 5 • Convert y = -x2 – 2x + 1 Vertex = (1, 3) Standard form: y = 2(x-1)2 + 3 Vertex = (-1, 2) Standard form: y = -(x+1)2 + 2

Homework Pg. 59 #23-33 odd

WARM UP Use f(x) = 3x 2 + 4x – 6 to evaluate the following. 1. f(2) 2. f(-4) 3. f(0)