Intro to Quadratics Unit 4 part 2 Lesson

Intro to Quadratics Unit 4 (part 2), Lesson 5 11/24/2014

Warmup �

EOC Review 1. 2. 3.

Warm Up: Use y = x 2 to fill in the table to the left & answer the questions What do you notice about the outputs? Why does this happen? If you plot each point what shape do you think it would make? Use y = x 2 to fill in the table to the left & answer the questions. X -3 -2 -1 0 1 2 3 Y What do you notice about the outputs? Why does this happen? If you plot each point what shape do you think it would make?

Quadratics �Polynomials of degree “ 2” �Graph forms a parabola Ex) y = x 2 – 3

Describing a Parabola �Roots: where graph crosses x-axis (x-intercepts / zeros) �Y-intercept: where graph crosses y-axis �Vertex: Maximum or Minimum point �Axis of Symmetry: line that divides parabola in half �End behavior: direction the “ends” of the parabola are pointing:

Roots: _________ Vertex: _________ Y-intercept: ________ Axis of Symmetry: ______ End behavior: _______ The Parabola Roots: Vertex: Y-intercept: “ROOT” VERTEX (Min) y-intercept

Axis of Symmetry: End Behavior: Axis of Symmetry

Ex 1) Graph and identify characteristics y = x 2 + 4 x X -5 -4 -3 -2 -1 0 1 Y

Characteristics �Roots: ____ �Y-intercept: ______ �Vertex ______ �Axis of Symmetry: ____ �End behavior: ______

Ex 2) Your Try! Graph and identify characteristics y = -x 2 - 2 x + 3 X Y -4 -3 -2 -1 0 1 2

Characteristics �Roots: ____ �Y-intercept: ______ �Vertex ______ �Axis of Symmetry: ____ �End behavior: ______

Warmup �Graph the quadratic y = x 2 – 2 x – 8 �Identify the: Vertex Axis of symmetry Roots End Behavior

EOC Review

More EOC Review

Ex 3) Sketch a graph that meets the following requirements: �Quadratic �Roots @ -3 and 1 �Vertex at (-1, 3)

Sketch a quadratic graph with roots at -5 and -2, and the end behavior is “down”

Sketch a quadratic graph that has NO ROOTS

Sketch a quadratic graph with y-intercept at (0, 3) and let this also be the vertex.

Sketch a quadratic graph with an axis of symmetry at x = 4

Sketch a graph with an axis of symmetry at x = 1, y -intercept of 3, and goes through (-1, 6)

Sketch a graph with a vertex at (-3, -2) and goes through the point (-6, -5)

Exit Ticket �Sketch a quadratic graph with a vertex at (-3, 4) and roots at -5 & 0. �Draw the axis of symmetry �Label the vertex as the “max” or “min”

P = -2. 5 s + 500 s - 1000 # phones Sold 0 20 40 60 80 100 120 140 160 180 200 Profit 1. Fill in the table 2. Graph your revenue vs. items sold (label your axes, go by 20’s) 3. Find the vertex & explain what this represents in context 4. Find the axis of symmetry and explain the importance of this line in context 5. Find the roots & explain what they represent in context of the problem