Aim #61: How do we graph quadratic equations from the vertex form?
Homework: handout
2-1-17
Do Now: a. Graph each of the following quadratic equations (you may use a
calculator to help you find points).
2
2
y=x
y = (x - 2)
vertex:
vertex:
y = (x + 2)
2
vertex:
b. How are the coordinates of the vertex for each graph similar? How are they
different?
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2
1. a. The graph of y = x is shown below. Consider the graph of y = (x − 4). Where
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would you expect this graph to be in relation to y = x? Sketch a graph of
2
y = (x - 4) .
b. What is the vertex of
2
y = (x - 4) ?
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c. Graph y = (x - 4) + 1 on the axes above. How does this graph relate to the
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graph of y = (x - 4) ? What is the vertex of this quadratic?
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2. a. Graph y = (x + 3) - 5 on the axes.
b. Describe how this quadratic equation
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relates to y = x , the parent function.
c. What is the vertex of y = (x + 3)
2
- 5?
d. How does the vertex relate to the
equation?
3. Without graphing, state the vertex for each of the following quadratic
equations.
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2
a. y = (x - 5) + 3
b. y = x - 25
c. y = (x + 4)
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4. Write a quadratic equation whose graph will have the given vertex.
a. (-2, 6)
b. (1.9, -4)
c. (0, 100)
d. (h, k)
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5. a. The graph of y = (x - 3) + 1 is shown below. Graph the following
quadratic equations on the same axes.
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y = 2(x - 3) + 1
y=
1
2
(x - 3) + 1
4
2
y = -4(x - 3) + 1
b. What do they all have in common?
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The vertex form of a quadratic equation is y = a(x - h) + k, where (h, k) is the
vertex.
Compared to when a = 1,
the graph is shrunk vertically when - 1 < a < 1 (the graph gets wider)
the graph is stretched vertically when a < -1 or a > 1 (the graph gets more narrow)
the graphs opens up when a is positive
the graph opens down when a is negative
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6. Compare the graphs of the function f(x) = -2(x + 3) + 2 and g(x) = 5(x + 3) + 2.
7. Write two different equations representing quadratic functions whose graphs
have vertices at (4.5, -8).
A quadratic equation in standard form can be converted into an equation in vertex
form by using completing the square.
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8. Convert to vertex form and then state the vertex:
y = x + 4x - 5
Let's sum it up
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The parent function of all quadratic equations is y = x .
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The vertex form of a quadratic equation is y = a(x - h) + k, where (h,k) are the
coordinates of the vertex. The a value gives us information about stretching,
shrinking, open up or open down.
A quadratic equation in standard form can be converted into vertex form by using
completing the square.