Key Features of Quadratic Functions

Key Features of Quadratic Functions

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​Forms of Quadratic Equations
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​Forms of Quadratic Equations
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​Forms of Quadratic Equations
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Multiple Choice

What form is this equation in?

$$y=-2\left(x+5\right)\left(x-6\right)$$

• Factored form

• Vertex Form

• Standard Form

• Slope Intercept Form

Multiple Choice

Which form should be used?

The quadratic function goes through the point (7,0) and has a vertex of (4,-4)

• Factored Form

• Vertex Form

• Point Slope Form

• Standard Form

Vertex Form should be used because the vertex was given.

Multiple Select

What does this form tell me?

$$y=-8x^2+2x+9$$

• The graph opens up

• The y intercept

• The vertex

• The graph opens down

• The x intercepts

Multiple Choice

Identify the transformations.

$$y=\frac{1}{5}\left(x-3\right)^2-6$$

• vertical stretch by a factor of 1/5, horizontal shift to the right 3, vertical shift down 6

• reflection across the x-axis, vertical stretch by a factor of 5, horizontal shift to the left 3, vertical shift up 6

• vertical compression by a factor of 1/5, horizontal shift to the right 3, vertical shift down 6

• reflection across the x-axis, vertical compression by a factor of 1/5, horizontal shift to the left 3, vertical shift down 6

​Key Features of Quadratic Functions
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​Vertex (h,k) Inside Opposite for h
Axis of Symmetry: x=h

If you have a MAXIMUM vertex, your graph is increasing then decreasing
If you have a MINIMUM vertex, your graph is decreasing then increasing

Vertex is (h, k) inside opposite for h so (-10,-8)

Multiple Choice

Does the graph have a maximum or minimum vertex?

• Maximum

• Minimum

​Key Features of Quadratic Functions
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Multiple Choice

What is the range of this function?

• $$y<2$$

• $$y\ge1$$

• $$y\le2$$

• $$y\le1$$

​Key Features of Quadratic Functions
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Intercepts:
Quadratics have a both x and y intercepts.
Positive/Negative Intervals:
You only use X VALUES to describe positive and negative intervals.
Use (,) only when stating intervals NEVER use [] (brackets)
Quadratics are POSITIVE, when the graph is ABOVE the x-axis

Quadratics are NEGATIVE, when the graph is BELOW the x-axis.

Multiple Select

What are the positive and negative intervals of this graph?

• Positive: $$\left(-\infty,-1\right]$$ and $$\left[3,\infty\right)$$

• Positive: $$\left(-\infty,-1\right)$$ and $$\left(3,\infty\right)$$

• Negative: $$\left(-1,3\right)$$

• Negative: $$\left[-1,3\right]$$

​Key Features of Quadratic Functions
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Increasing/Decreasing Intervals:
You only use X VALUES to describe increasing and decreasing intervals.
Use (,) only when stating intervals NEVER use [] (brackets)
Quadratics are INCREASING, when the graph is GOING UP THE ROLLERCOASTER

Quadratics are DECREASING, when the graph is GOING DOWN THE ROLLERCOASTER

Copy this example of increasing and decreasing

Multiple Choice

True or False. This graph is decreasing when $$x>1$$

• True

• False

Multiple Choice

True or False

Quadratic Functions are ODD functions.

• True

• False

​Key Features of Quadratic Functions
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