UNIT 1 REVIEW of TRANSFORMATIONS of a GRAPH f(x) Original (Parent) Graph a•f(x – h) + k Transformed Graph “a” – value “h” – value “k” – value For graphs #1, 2, 3, 5, 8: y = x2 QUADRATIC FUNCTION (ORIGINAL) y = a(x – h)2 + k TRANSFORMED QUADRATIC FUNCTION

FIND THE EQUATION for Graphs #1, 2, 3: 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

FIND THE EQUATION for graphs #5, 8: y = a(x – h)2 + k Graph #8: y = a(x – h)2 + k

“a” – value “h” – value “k” – value For graphs #4, 6, 7, and 9: “Sideways Quadratic Graphs” 1) If you look at the symmetrical parts of these graphs above or below the axis of symmetry, what function do these parts most resemble? 2) Write down the general equation of the parent function and transformed function? SQUARE ROOT FUNCTION (ORIGINAL) TRANSFORMED SQUARE ROOT FUNCTION “a” – value “h” – value “k” – value

FIND THE EQUATION for Graphs #4 ,6: Step #1: Use the vertex of the graph to indicate the horizontal (h) and vertical (k) changes for the starting pt. Step #2: Use another point on the graph to determine the “a”- value Step #3: Solve the transformed equation for x Graph #4: Graph #6:

FIND THE EQUATION for Graphs #7 ,9:

Look at the equations for graphs #4, 6, 7, 9 OBSERVATIONS: Look at the equations for graphs #4, 6, 7, 9 Do you notice any SIMILARITIES or DIFFERENCES in those equations in comparison to the quadratic? How are the coordinates of the VERTEX in the graph related to the equation? How is the axis of symmetry equation and vertex related based on the shape of the graph?

a (+ up; – down) a (+ right; –left) Vertex Form Vertex Form Vertex: Parabola Formulas Summary of Day One Findings Parabolas (Type 1: Up and Down) 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 into appropriate vertex form equation and use another point to solve for “a”. [A] Opening Vertical Vertex: (2, 4) Point: (-6, 8) [B] Opening: Horizontal Vertex: (- 4, 6) Point: (2, 8)

COMPLETING THE SQUARE REVIEW Find the value to add to the trinomial to create a perfect square trinomial: (Half of “b”)2 [A] [B] [C] [D]

FIND VERTEX FORM given STANDARD FORM VERTEX FORM: DAY TWO FIND VERTEX FORM given STANDARD FORM Method #1: COMPLETING THE SQUARE Find the value to make a perfect square trinomial to the quadratic equation. (Be careful of coefficient for x2 which needs to be distributed out) ADD ZERO by adding and subtracting the value to make a perfect square trinomial so as to not change the overall equation (Be careful of coefficient for x2 needs multiply by subtraction)

Example 1 Type 1: Up or Down Parabolas Write in vertex form. Identify the vertex and axis of symmetry. [B] [A] Vertex: (-3, -6) Vertex: (2, -1) Axis: x = -3 Axis: x = 2

Example 2 Type 2: Right or Left Parabolas Write in vertex form. Identify the vertex and axis of symmetry. [B] [A] Vertex: (-5, 3) Vertex: (-8, -4) Axis: y = 3 Axis: y = -4

Example 3 Type 1: Up or Down Parabolas Write in standard form. Identify the vertex and axis of symmetry. [B] [A] Vertex: (-1, 4) Vertex: (-1, 4) Axis: x = -1 Axis: x = -1

Example 4 Type 2: Right or Left Parabolas Write in vertex form. Identify the vertex and axis of symmetry. [B] [A] Vertex: (13, -2) Vertex: y = -2 (-25/2, -97/4 ) Axis: y = -97/4 Axis:

Method #2: SHORTCUT Find the AXIS of SYMMETRY : Axis is horizontal or vertical based on shape Find VERTEX (h, k) of STANDARD FORM “a” – value for vertex form should be the same coefficient of x2 in standard form. Check by using another point (intercept)

Vertex: (5, - 5) Vertex: (- 4, -15) Axis: x = 5 Axis: x = - 4 PRACTICE METHOD #2: Slide 2 Write in vertex form. Find vertex and axis of symmetry. [1] [2] Vertex: (5, - 5) Vertex: (- 4, -15) Axis: x = 5 Axis: x = - 4

Vertex: (-4, 0) Vertex: (1, 2) Axis: x = -4 Axis: x = 1 PRACTICE METHOD #2: Slide 2 Write in vertex form. Find vertex and axis of symmetry. [3] [4] Vertex: (-4, 0) Vertex: (1, 2) Axis: x = -4 Axis: x = 1

Vertex: (-41/5, - 5/2) Vertex: (3, -2) Axis: y = -5/2 Axis: y = -2 PRACTICE METHOD #2: Slide 3 Write in vertex form. Find vertex and axis of symmetry. [5] [6] Vertex: (-41/5, - 5/2) Vertex: (3, -2) Axis: y = -5/2 Axis: y = -2

Vertex: (-3, -2) Vertex: (31/4, -3/2) Axis: y = -2 Axis: y = -3/2 PRACTICE METHOD #2: Slide 4 Write in vertex form. Find vertex and axis of symmetry. [7] [8] Vertex: (-3, -2) Vertex: (31/4, -3/2) Axis: y = -2 Axis: y = -3/2