Section 5.2--Parabola Parts
Objective: To be able to find/identify the vertex of a parabola, to identify and graph the axis of symmetry and the y­intercept, and to identify the direction the parabola opens. Direction the parabola opens......
look ________________ found in front of ________________.
Equations for a parabola come in two forms: y = a(x - h)2 + k
With numbers in the equations they look like this:
y = ax2 + bx + c
or
y = 3(x + 4)2 + 5
or
y = 2x2 + 4x - 7
What direction are the equations opening?
y = 3(x + 4)2 + 5
y = 2x2 + 4x - 7
y = -x2 - 5x - 2
y = -4(x - 3)2 - 1
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To identify the vertex of a parabola...
y = a(x - h)2 + k
With numbers in the equations they look like this:
y = 3(x + 4)2 + 5
or
or
y = ax2 + bx + c
y = 2x2 + 4x - 7
Vertex in y = 3(x + 4)2 + 5 is found by taking the ___________ of what in
the parentheses and ___________ the value added or subtracted from
parentheses.
y = -4(x - 3)2 - 1
y = 2(x + 4)2 + 5
y = (x - 2)2 + 6
2
Vertex in y = 2x2 + 4x - 7 is found by identifying a, b, and c. Once identified, place
values into _________________. After you have the value for x, place back into the
equation for x and solve for y.
y = 2x2 + 4x - 7
y = -x2 - 5x - 2
y = 3x2 + 3x + 1
3
To identify the y­intercept....
If the equation is in the form y = ax2 +bx + c, the y-intercept is
_________ and ALWAYS written as a _____________.
y = 2x2 + 4x - 7
y = -x2 - 5x - 2
y = 3x2 + 3x + 1
If the equation is in the form y = a(x - h)2 + k, the y-intercept is
found by first _____________ ( _________ method--see next
slide for practice) the equation out then following the above steps
to identify the y-intercept.
y = -4(x - 3)2 - 1
y = 2(x + 4)2 + 5
y = (x - 2)2 + 6
4
Practice of ___________ Method
(x - 2)(x + 4)
(x - 5)(x - 5)
(x + 1)(x + 8)
(x + 2)2
3(x - 1)2
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Homework...
p. 328 13, 14, 18‐20
Directions for the above problems...
Find the y‐intercept, the vertex, and
identify the direction in which the parabola
opens. Now sketch (ON GRAPH PAPER)
the parabola with all the above information
identified on the sketch.
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To identify the axis of symmetry....
One must first identify the _____________ of the equation. Once the vertex is
known the axis of symmetry is found by using the x-coordinate of the vertex.
Axis of symmetry is ALWAYS in an equation of ____________.
y = -4(x - 3)2 - 1
y = 2(x + 4)2 + 5
y = -x2 - 5x - 2
y = 2x2 + 4x - 7
7
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Homework...
p. 328 13, 14, 18‐20
Directions for the above problems...
Find the y‐intercept, the vertex, and identify the
direction in which the parabola opens. Now
sketch (ON GRAPH PAPER) the parabola with all
the above information identified on the sketch.
Now add to the assignment above....
Find the axis of symmetry of each problem above.
Add problems 30 and 31 to the assignment also.
Follow directions for the problems found in the
book.
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