Algebra 2: Unit 3 - Vertex Form

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Presentation transcript:

Algebra 2: Unit 3 - Vertex Form UNIT 1 REVIEW of TRANSFORMATIONS of a GRAPH f(x) Original (Parent) Graph a•f(x – h) + k Transformed Graph “a” – value Stretch or Shrink Graph and Flips for negative “h” – value Shifts the Graph Right or Left “k” – value Shifts the Graph Up or Down For quadratic graphs #1 - 6: y = a(x – h)2 + k TRANSFORMED QUADRATIC FUNCTION y = x2 QUADRATIC FUNCTION (ORIGINAL)

FIND THE EQUATION of the Quadratics in Graphs #1 - 6 Step #1: Use the vertex to indicate the horizontal (h) and vertical (k) changes Step #2: Use another point on the graph to help determine the “a”- value (Hint: The direction it opens indicates the sign) Graph #1: y = a(x – h)2 + k Graph #2: y = a(x – h)2 + k

Graph #3: y = a(x – h)2 + k Graph #4: y = a(x – h)2 + k

Graph #5: y = a(x – h)2 + k Graph #6: y = a(x – h)2 + k

a (+ up; – down) a (+ right; –left) Vertex Form Vertex Form Vertex: QUADRATIC FUNCTIONS – VERTEX FORM SUMMARY Vertical Parabolas (Type 1: Up and Down) Horizontal Parabolas (Type 2: Right and Left) Vertex Form Vertex Form Vertex: Vertex: (h, k) (h, k) Axis: x = h Axis: y = k Rate: a (+ up; – down) Rate: a (+ right; –left)

Find VERTEX FORM EQUATION: Given Vertex & Point Plug vertex (h, k) into appropriate vertex form equation and use another point (x, y) to solve for “a”. [A] Opening Vertical Vertex: (2, 4) Point: (-6, 8) [B] Opening: Horizontal Vertex: (- 4, 6) Point: (2, 8)

Vertex Form to Standard Form of Quadratic Functions FOIL the squared statement. Distribute a-value Combine Like Terms [B] [A]

[D] [C]

Algebra 2: Unit 3 - Vertex Form Standard Form to Vertex Form of Quadratic Functions Vertical Parabolas ( y = ) Graph the Equation in [Y =] Find Vertex using MIN or MAX command in [CALC] a – value is the same in standard and vertex form. [B] [A] a - value: a - value: Vertex: Vertex: Equation: Equation:

Horizontal Parabolas ( x = ) Vertical Parabolas ( y = ): Continued [D] [C] a - value: a - value: Vertex: Vertex: Equation: Equation: Horizontal Parabolas ( x = ) Switch the variables and Graph the Equation in [Y =] Opens Up = Opens Right Opens Down = Opens Left Find Vertex using MIN or MAX command in [CALC] Switch the Min or Max Ordered Pair for actual vertex a – value is the same in standard and vertex form.

Horizontal Parabolas Practice a - value: a - value: Sketch: Sketch: Vertex: Vertex: Equation: Equation:

a - value: a - value: Sketch: Sketch: Vertex: Vertex: Equation: [D] [C] a - value: a - value: Sketch: Sketch: Vertex: Vertex: Equation: Equation: