Topics
2. Quadratic Functions and Models
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United States of America
Grades 9-12

2.03 Quadratic functions in vertex form

Lesson
Practice
Adaptive
Worksheet

Interactive practice questions

Consider the function $y=5\left(x-\frac{1}{2}\right)^2-\frac{1}{4}$y=5(x−12​)2−14​.

a

Write down the coordinates of the vertex.

Vertex: $\left(\editable{},\editable{}\right)$(,)

b

Find the equation of the vertical axis of symmetry for this parabola.

c

Write down the coordinates of the $y$y-intercept. Leave your answer in simplest fractional form.

$y$y-intercept: $\left(\editable{},\editable{}\right)$(,)

Easy
1min

The graph of $y=\left(x-1\right)^2$y=(x−1)2 is translated $4$4 units up.

Easy
2min

The graph of $y=-\left(x+5\right)^2$y=−(x+5)2 is translated $4$4 units up.

Easy
3min

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

Easy
1min
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Outcomes

A.SSE.B.3.B

Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.

A.CED.A.2

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

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. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.

F.IF.C.7

Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

F.IF.C.7.A

Graph linear and quadratic functions and show intercepts, maxima, and minima.

F.IF.C.8

Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

F.IF.C.8.A

Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

F.BF.A.1

Write a function that describes a relationship between two quantities.

F.BF.A.1.A

Determine an explicit expression, a recursive process, or steps for calculation from a context.

F.BF.B.3

Identify the effect on the graph of replacing f(x) by f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

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