Graphing Quadratic Functions in Standard Form

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Graphing Quadratic Functionsin Standard Form
y ax2 bx c
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Quadratic Functions
The graph of a quadratic function is a parabola.
A parabola can open up or down.
If the parabola opens up, the lowest point
(minimum) is called the vertex.
If the parabola opens down, the vertex is the
highest point (maximum).
NOTE if the parabola opened left or right it
would not be a function!
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Standard Form
The standard form of a quadratic function is
y ax2 bx c
The parabola will open up when the a value is
positive.
The parabola will open down when the a value is
negative.
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Line of Symmetry
Parabolas have a symmetric property to them.
If we drew a line down the middle of the
parabola, we could fold the parabola in half.
We call this line the line of symmetry.
The line of symmetry ALWAYS passes through the
vertex.
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Finding the Line of Symmetry
When a quadratic function is in standard form
For example
Find the line of symmetry of y 3x2 18x 7
y ax2 bx c,
The equation of the line of symmetry is
This is best read as the opposite of b divided
by the quantity of 2 times a.
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Finding the Vertex
For example, Find the vertex y 2x2 8x 3
We know the line of symmetry always goes through
the vertex.
Thus, the line of symmetry gives us the x
coordinate of the vertex.
To find the y coordinate of the vertex, we need
to plug the x value into the original equation.
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A Quadratic Function in Standard Form
The standard form of a quadratic function is
given by y ax2 bx c
STEP 1 Find the line of symmetry
STEP 2 Find the vertex
STEP 3 Make a table of values using x values
close to the line of symmetry. (Put the vertex in
the middle of your table of values.)
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A Quadratic Function in Standard Form

• Example 1
• a. Graph
• Find and label the axis of symmetry.
• Find the maximum/minimum
• Find the domain range
• y 2x2 4x 1

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A Quadratic Function in Standard Form

• Example 2
• a. Graph
• Find and label the axis of symmetry.
• Find the maximum/minimum
• Find the domain range
• y x2 - 2x 1

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A Quadratic Function in Standard Form

• Example 3
• a. Graph
• Find and label the axis of symmetry.
• Find the maximum/minimum
• Find the domain range
• y -1/6x2 x 3