 # GRAPHING QUADRATIC FUNCTIONS VERTEX FORM Goal: I can complete the square in a quadratic expression to reveal the maximum or minimum value. (A-SSE.3b)

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GRAPHING QUADRATIC FUNCTIONS VERTEX FORM Goal: I can complete the square in a quadratic expression to reveal the maximum or minimum value. (A-SSE.3b)

VOCABULARY:  Parabola-  Vertex-  Axis of symmetry- The U-shaped graph of a quadratic function The highest (maximum) or lowest (minimum) point on a parabola The vertical line that passes through the vertex and divides the parabola into 2 equal parts

VERTEX FORM OF A QUADRATIC FUNCTION Given the function y = a(x – h) 2 + k  If a > 0, the parabola opens up  If a < 0, the parabola opens down  The axis of symmetry is x = h  The vertex is (h, k)

VERTEX FORM OF A QUADRATIC FUNCTION

EXAMPLE  Determine the a to decide if the parabola opens up or down or it’s a minimum or maximum, the coordinates of the vertex and the line of symmetry.  Now let’s Graph!

2. Make a table of values: EXAMPLE FILL IN THE TABLE OF VALUES TO GRAPH THE QUADRATIC. XY vtx -2 -5 -4 -3 y = (-5 +3) 2 + 2 6 3 2 3 6 y = (-4 +3) 2 + 2 y = (-2 +3) 2 + 2 y = (-1 +3) 2 + 2  Now let’s Graph! 3. Plot points:

EXAMPLE  Determine the a to decide if the parabola opens up or down or it’s a minimum or maximum, the coordinates of the vertex and the line of symmetry.  Now let’s Graph!

2. Make a table of values: EXAMPLE FILL IN THE TABLE OF VALUES TO GRAPH THE QUADRATIC. XY vtx -4 -3 -2 0 y = (-4 +2) 2 - 6 -2 -5 -6 -5 -5 -2 y = (-3 +2) 2 - 6 y = (-1 +2) 2 - 6 y = (0 +2) 2 - 6  Now let’s Graph! 3. Plot points:

EXAMPLE  Determine the a to decide if the parabola opens up or down or it’s a minimum or maximum, the coordinates of the vertex and the line of symmetry.  Now let’s Graph!

2. Make a table of values: EXAMPLE FILL IN THE TABLE OF VALUES TO GRAPH THE QUADRATIC. XY vtx 4 1 2 3 5 y = -4(1 -3) 2 -16 -4 0 -4 -4 -16 y = -4(2 -3) 2 y = -4(4 -3) 2 y = -4(5 -3) 2  Now let’s Graph! 3. Plot points:

CHANGE A QUADRATIC FUNCTION FROM STANDARD FORM TO VERTEX FORM  Move the constant  Add (b/2) 2 to each side  Factor the perfect square trinomial  Write in the form y = a(x – h) 2 + k  Now let’s Graph!

2. Make a table of values: EXAMPLE FILL IN THE TABLE OF VALUES TO GRAPH THE QUADRATIC. XY vtx -4 -3 -2 0 y = (-4 +2) 2 + 2 6 3 2 3 6 y = (-3 +2) 2 + 2 y = (-1 +2) 2 + 2 y = (0 +2) 2 + 2  Now let’s Graph! 3. Plot points:

WRITE THE QUADRATIC IN VERTEX FORM  Move the constant  Add (b/2) 2 to each side  Factor the perfect square trinomial  Write in the form y = a(x – h) 2 + k  Now let’s Graph!

2. Make a table of values: EXAMPLE FILL IN THE TABLE OF VALUES TO GRAPH THE QUADRATIC. XY vtx 3 0 1 2 4 y = (0 -2) 2 - 5 -4 -5 -4 -4 y = (1 -2) 2 - 5 y = (3 -2) 2 - 5 y = (4 -2) 2 - 5  Now let’s Graph! 3. Plot points:

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