Download 5.7A Vertex Form Parabola

Algebra 2
5.7A Analyzing Graphs of Quadratic Functions
Obj: able to complete the square to write the vertex form of a quadratic function and to graph a parabola.
5.7A Cooperative Learning
DIRECTIONS: With your partner, work out the following problems. You both need to record answers on your own
page as you work together.
Turn to page 284 in your text and get out your graphing calculator.
Complete Activity 1.
Graph y = x2, y = x2 + 3, and y = x2 – 5
What happens to the graph of y = x2 when a value is added to or subtracted from the squared term?
Complete Activity 2.
Graph y = x2, y = (x + 3)2, and y = (x – 5)2
What happens to the graph of y = x2 when a value is added to or subtracted from the value x?
Complete Activity 3a
Graph y = x2 and y = -x2
What happens to the graph of y = x2 when it is multiplied by a negative value?
Complete Activity 3b
Graph y = x2 and y = 4x2
What happened?
Graph y = x2 and y =
What happened?
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x
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5.7A Analyzing Graphs of Quadratic Functions
The vertex form of a quadratic function is y = a(x – h)2 + k, with a ≠ 0.
The axis of symmetry for the parabola of a quadratic function in vertex form is x = h .
The vertex of a quadratic function in vertex form is the point ( ____ , ____ ).
The parent function for a quadratic function in vertex form is y = x2.
Transformations:
When a < 0, the graph is reflected across the ____ -axis.
When 0 < a < 1, the graph is _____________ by a factor of a.
When a > 1, the graph is _____________ by a factor of a.
When h > 0, the graph shifts _________ h units.
When k > 0, the graph shifts _________ k units.
When h < 0, the graph shifts _________ h units.
When k < 0, the graph shifts _________ k units.
To graph a quadratic function of the form y = a(x – h)2 + k:
1. Graph the vertex, (h, k).
2. Draw the axis of symmetry as a dashed vertical line.
3. Find and graph the y-intercept and its reflection across the axis of symmetry.
4. Evaluate the function for another value of x. Graph the point and its reflection.
5. Sketch the curve.
Graph the following quadratic function
Complete the square to write the equation
written in vertex form.
in vertex form and then analyze.
1. y = (x + 3)2 – 1
2. y = x 2 – 6x + 1
y = (x 2 – 6x +______) + 1 – ______
Vertex____________
Axis of Symmetry____________
y-intercept_______________
reflection of y-intercept__________
3. y = x 2 + 10x – 7
I have no clue what to do
even if somebody is
explaining the problem to me
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What do I still need to work on
Rate yourself on how well you understood this lesson.
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walking me through the
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