Warm Up Find five points and use them to graph Hint, use an x-y table to help you.

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Presentation transcript:

Warm Up Find five points and use them to graph Hint, use an x-y table to help you

11-1 G RAPHING Q UADRATIC F UNCTIONS Objective: To find and use the axis of symmetry and the vertex of a parabola to graph it. Standard 21.0

G RAPH FOR W ARM U P This “U” shape is called a parabola. Quadratic Function: y = Ax 2 + Bx + C A,B,C are integers Axis of Symmetry Cuts parabola in half Reflects over line x = 0 Vertex Turning point (0,0) On axis of symmetry Magic Ordered Pairs (1,1a) (2,4a) (3,9a) Use these every time When A,B,C change, moves vertex but does not change the shape

Looks like.. A parabola can also make shape. To tell which way it points, look at the a value a (+) = + + minimum (vertex) A (-) = – – maximum (vertex)

Examples Standard Form Opens Up or Down Find the axis of symmetry Find the vertex Graph using the parent function y = ax 2 + bx + c a(+) = up/min a(-) = down/max x = – b 2a Plug in x to standard form (1,1) (2,4) (3,9) reflect y = x 2 “Parent function” y = 1x 2 + 0x + 0 a = 1 b = 0 c = 0 Up Vertex Minimum x = 0 2(1) x = 0 y = (0) 2 y = 0 (0,0) This is the same graph as the warm up!

“11-1 Graphing Quadratic Functions” Worksheet Follow along and fill in the worksheet with me. We will graph 3 parabolas today in class You will complete tonight’s homework on a similar worksheet so… Take good notes in class so you can use them to help you do the homework!

HOMEWORK See problems below: 1) y = x 2 + 4x + 3 2) y = -x 2 + 4x – 1 3) y = x 2 + 6x + 9 4) y = -x 2 – 3 5) y = x 2 – 4x To be done on worksheet given in class Answers include: Up/down? Min/Max? Axis of Symmetry Vertex Graph

Extra Practice! The following 2 parabolas can be graphed and studied for extra practice

Examples Standard Form Opens Up or Down Find the axis of symmetry Find the vertex Graph using the parent function ax 2 + bx + c = y a(+) = up a(-) = down x = – b 2a Plug in x to standard form (1,1) (2,4) (3,9) reflect y = x 2 – 2x – 3 a = 1 b = -2 c = -3 Up Vertex Minimum x = -(-2) 2(1) x = 1 y = (1) 2 – 2(1) – 3 y = 1 – 2 – 3 y = -4 (1,-4)

Examples Standard Form Opens Up or Down Find the axis of symmetry Find the vertex Graph using the parent function ax 2 + bx + c = y a(+) = up a(-) = down x = – b 2a Plug in x to standard form (1,1) (2,4) (3,9) reflect y = x 2 + 4x + 4 a = 1 b = 4 c = 4 Up Vertex Minimum x = -(4) 2(1) x = -2 y = (-2) 2 + 4(-2) + 4 y = 4 – 8 +4 y = 0 (-2,0)