Algebra II Quarter 2: Handout #6
Name ________________________ Date _____________ Period _____
5.1 Graphing Quadratic Functions
Notes
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A quadratic function has the standard form y = ax2 + bx + c, where a ≠ 0.
The graph of a quadratic function is a parabola (“U-Shaped”).
The lowest (minimum) or highest (maximum) point on a parabola is called the
vertex.
The axis of symmetry for a parabola is the vertical line going through the
vertex.
How to graph a quadratic function in standard form, y = ax2 + bx + c:
o The parabola opens up if a > 0 and has a minimum.
o The parabola opens down if a < 0 and has a maximum.
o If |a| > 1, then the parabola become more narrow. (Opposite of intuition.)
o If |a| < 1, then the parabola becomes wider. (Opposite of intuition.)
−b
o The x-coordinate for the vertex can be found using the formula:
2a
o Once you have the x-coordinate for the vertex, substitute it back into the
given equation and solve for the y-coordinate.
o Axis of symmetry is the vertical line: x =
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−b
2a
How to graph a quadratic function in Vertex form, y = a(x – h)2 + k:
o Vertex is (h, k)
o Axis of symmetry is x = h
o The parabola opens up if a > 0 and has a minimum.
o The parabola opens down if a < 0 and has a maximum.
o If |a| > 1, then the parabola become more narrow. (Opposite of intuition.)
o If |a| < 1, then the parabola becomes wider. (Opposite of intuition.)
Algebra II Quarter 2: Handout #6
Examples
1. Write the quadratic function in standard form:
a. y = –(x + 4)(x – 9)
b. y = 3(x – 1)2 + 8
Algebra II Quarter 2: Handout #6
2. Graph the quadratic functions:
a. y = x2 – 8x + 6
i. Graph characteristics:
1. Vertex: _________________________
2. Axis of Symmetry: ____________________
3. Open up or down?: ______________________
4. Narrow, Wide, Normal?: ______________________
Algebra II Quarter 2: Handout #6
b. –(x + 2)(x – 4)
i. Graph characteristics:
1. Vertex: _________________________
2. Axis of Symmetry: ____________________
3. Open up or down?: ______________________
4. Narrow, Wide, Normal?: ______________________
Algebra II Quarter 2: Handout #6
c. y = 4(x – 1)2 + 5
i. Graph characteristics:
1. Vertex: _________________________
2. Axis of Symmetry: ____________________
3. Open up or down?: ______________________
4. Narrow, Wide, Normal?: ______________________