Graphs of Quadratic Equations

43210 In addition to level 3, students make connections to other content areas and/or contextual situations outside of math. Students will factor polynomials using multiple methods, perform operations (excluding division) on polynomials and sketch rough graphs using key features. - Factor using methods including common factors, grouping, difference of two squares, sum and difference of two cubes, and combination of methods. - Add, subtract, and multiply polynomials, - Explain how the multiplicity of the zeros provides clues as to how the graph will behave. - Sketch a rough graph using the zeros and other easily identifiable points. Students will factor polynomials using limited methods, perform operations (excluding division) on polynomials, and identify key features on a graph. - Add and subtract polynomials. - Multiply polynomials using an area model. - Factor polynomials using an area model. - Identify the zeros when suitable factorizations are available. - Identify key features of a graph. Students will have partial success at a 2 or 3, with help. Even with help, the student is not successful at the learning goal. Focus 9 Learning Goal – ( HS.A-SSE.A.1, HS.A-SSE.A.2, HS.A-SEE.B., HS.A-APR.A.1, HS.A- APR.B.3, HS.A-REI.B.4) = Students will factor polynomials using multiple methods, perform operations (excluding division) on polynomials and sketch rough graphs using key features.

Standard Form: y = ax 2 +bx+ c Shape: Parabola Vertex: highest or lowest point of the graph.

Axis of Symmetry: Line that divides parabola into two parts that are mirror image of each other. Axis of Symmetry Vertex

The vertex has an x-coordinate of The axis of symmetry is the vertical line passing through

y = x 2 First find the vertex. This is the x value of the vertex, now find the y value. If x = 0, y = 0 Vertex = (0,0) 0 is the axis of symmetry:

Example: y = x 2 Make a table for y = x 2 Since the vertex is (0,0), pick an x value to the right and left of 0.

To graph a Quadratic Equation y = ax 2 +bx+cy = -ax 2 +bx+c If a is positive, the parabola opens up If a is negative, the parabola opens down

Graph Points Line of symmetry A is positive 1, so the parabola opens up with (0,0) as the low point.

GRAPH: y = x 2 -x-6 Identify the a, b, and c values First find the vertex Make a table with an x value to the right and left of the vertex x value Graph these points and connect. Label the vertex

Find vertex and plug in to find y. value to have high or low point. 1.

The x value of the vertex is 1 / 2 Now find the y value of the vertex by plugging x back into the equation. y = x 2 -x-6 y = ( 1 / 2 ) 2 – ½ - 6 The y value is - 25 / 4. Now pick a point to the left and right of ½.

GRAPH : y = x 2 -x-6 I try to pick points equal distance from the vertex x value. I also tried 0 here.

Vertex low Y=x 2 -x-6 opens up (a positive) line of symmetry x =

Line of Symmetry Graph: y= -2x 2 +2x+1 a is negative- opens down = 1 2 Find the y value, then pick a point to the left and right of 1 / 2 to see how to draw the parabola.

y=-2x 2 +2x+1