Quadratic Functions: Key Features

Define Maximum

• The highest or lowest point on the graph

• The highest y-value on the graph

• The lowest y-value on the graph

• A line that divides the graph into two equal parts. i.e. cuts the graph in half

Answer explanation

If the parabola opens down, then the top is the maximum.

Which function has a maximum at (2, 0)?

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Determine the domain and range of the function

• Domain: All real numbers, Range: All real numbers

• Domain: x ≥ -4, Range: All real numbers

• Domain: All real numbers, Range: y ≥ -4

• Domain: -1 ≤ x ≤ 5, Range: y ≥ -4

Define Axis Of Symmetry

• A line that divides the graph into two equal parts. i.e. runs through the center of the parabola

• Where the parabola touches or intersects the x-axis, also called the x-intercept

• The highest y-value on the graph

• The highest or lowest point on the graph

Which function has an axis of symmetry of x = 0?

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• None of the above

What is the equation of the axis of symmetry?

• y = 0

• x = 0

• x = 3

• x = -3

Which function has a range y ≥ -4?

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• None of the above

If a function has a MINIMUM, which way does it OPEN?

• Down (Umbrella)

• Up (Tea Cup)

• To the right (like the letter “c”)

Define Vertex

• Where the parabola touches or intersects the x-axis

• The highest or lowest point on the graph

• Where parabola line touches or intersects the x- axis, also called the x-intercept

• A line that divides the graph into two equal parts. i.e. cuts the graph in half

Define Roots, Zeros, X-intercept, and Solutions

• Where the parabola touches or interests the x-axis

• Where the parabola touches or interests the y-axis