Quadratic Functions Review

Vocabulary

1

The shape of the graph of a quadratic function:

Parabola

1

The parent function of the Quadratic family:

f(x)  =  x²

1

The imaginary line that cuts a quadratic graph in half:

Axis of Symmetry

1

The term(s) to describe whether the vertex is the highest or lowest point of a quadratic graph:

Maximum and Minimum

Transformations

1

Describe the transformation(s)

f(x)  =  x² + 3

Translated up 3

1

Describe the transformation(s)

g(x)  =  -(1/2)x²

Reflected over the x-axis

Vertically compressed by a factor of 1/2

1

Describe the transformation(s)

h(x)  =  (x - 9)² - 5

Translated to the right 9

Translated down 5

1

f(x)  =  5(x - 6)² + 2

Stretched vertically by a factor of 5

Translated to the right by 6

Translated up 2

Quadratic Functions

1

Write the following quadratic equation in Standard Form:

4x - 5  =  3x² - 2x

3x²  -  6x  +  5  =  0

or

0  =  -3x²  +  6x  -  5

1

This expression, part of the famous Quadratic Formula, is known as the "Discriminant". 

b² - 4ac

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What value would c need to be in order to "complete the square"?

x² - 14x + c

c = 49

1

What are the coordinates of the vertex of the following parabola?

y  =  3x² - 24x + 49

(4, 1)

Number of Solutions

1

A quadratic graph crosses the x-axis in two different places.

2 solutions

1

The value of the Discriminant is negative.

Zero solutions

1

A quadratic function has a "Double Root" at 5.

1 solution

1

a  =  -9

b  =  12

c  =  6

1 solution

Solving

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x² - 9  =  0

x  =  -3 or 3

1

(x + 5)²  =  36

x  =  -11 or 1

1

x² - 4x + 3  =  0

x  =  1 or 3

1

2x² - 8x - 10  =  0

x  =  -1 or 5