Topics
7. Quadratic Functions
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United States of AmericaTennessee
Algebra 1

7.02 Characteristics of quadratic functions

Lesson
Practice
Adaptive
Worksheet

Interactive practice questions

Consider the graph of the function $y=f\left(x\right)$y=f(x) and answer the following questions.

Loading Graph...
A parabola facing upward on a coordinate plane with the turning point at (-4,0)

 

a

What is the absolute minimum of the graph?

b

Hence determine the range of the function.

$y\ge\editable{}$y≥

c

Over what interval of the domain is the function decreasing?

$x<\editable{}$x<

Easy
< 1min

Consider the equation $y=\left(x-3\right)^2$y=(x−3)2.

Easy
2min

Consider the equation $y=\left(x-3\right)^2-16$y=(x−3)2−16.

Easy
2min

Consider the function $y=x^2-2x-3$y=x2−2x−3.

Easy
< 1min
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Outcomes

A1.N.Q.A.1

Use units as a way to understand real-world problems.*

A1.N.Q.A.1.A

Choose and interpret the scale and the origin in graphs and data displays.*

A1.A.REI.D.5

Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

A1.F.IF.B.4

For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.*

A1.F.IF.B.5

Relate the domain of a function to its graph and, where applicable, to the context of the function it models. *

A1.F.IF.B.6

Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate and interpret the rate of change from a graph.*

A1.F.IF.C.7

Graph functions expressed algebraically and show key features of the graph by hand and using technology.*

A1.F.IF.C.9

Compare properties of functions represented algebraically, graphically, numerically in tables, or by verbal descriptions.*

A1.MP1

Make sense of problems and persevere in solving them.

A1.MP2

Reason abstractly and quantitatively.

A1.MP3

Construct viable arguments and critique the reasoning of others.

A1.MP4

Model with mathematics.

A1.MP6

Attend to precision.

A1.MP7

Look for and make use of structure.

A1.MP8

Look for and express regularity in repeated reasoning.

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