# Shifting Curves

In this worksheet, students must identify the equation of a curve after it has been transformed or shifted.

Key stage:  KS 4

Curriculum topic:  Algebra

Difficulty level:

### QUESTION 1 of 10

All are parabolic but their equations can be used to identify their shapes quickly and easily.

We start with the basic function f(x) = x², or the graph of the parabola y = x².

Vertical shifts

We get equations of the form  y = x² ± k

Horizontal shifts

We get equations of the form  y = (x ± k)²

Stretching

We get equations of the form  y = kx²

What shape are these curves?

parabolas

hyperbolas

squared

Select the correct equation which is represented by graph B.

y = x²

y = 2x²

y = 3x²

y = (x - 3)²

y = (x - 2½)²

y = (x + 1)²

y = x² - 3

y = (x + 3)²

y = x² + 2

Select the correct equation which is represented by graph C.

y = x²

y = 2x²

y = 3x²

y = (x - 3)²

y = (x - 2½)²

y = (x + 1)²

y = x² - 3

y = (x + 3)²

y = x² + 2

Select the correct equation which is represented by graph B.

y = x²

y = 2x²

y = 3x²

y = (x - 3)²

y = (x - 2½)²

y = (x + 1)²

y = x² - 3

y = (x + 3)²

y = x² + 2

Select the correct equation which is represented by graph A.

y = x²

y = 2x²

y = 3x²

y = (x - 3)²

y = (x - 2½)²

y = (x + 1)²

y = x² - 3

y = (x + 3)²

y = x² + 2

Select the correct equation which is represented by graph A.

y = x²

y = 2x²

y = 3x²

y = (x - 3)²

y = (x - 2½)²

y = (x + 1)²

y = x² - 3

y = (x + 3)²

y = x² + 2

Select the correct equation which is represented by graph A.

y = x²

y = 2x²

y = 3x²

y = (x - 3)²

y = (x - 2½)²

y = (x + 1)²

y = x² - 3

y = (x + 3)²

y = x² + 2

Select the correct equation which is represented by graph B.

y = x²

y = 2x²

y = 3x²

y = (x - 3)²

y = (x - 2½)²

y = (x + 1)²

y = x² - 3

y = (x + 3)²

y = x² + 2

Select the correct equation which is represented by graph C.

y = x²

y = 2x²

y = 3x²

y = (x - 3)²

y = (x - 2½)²

y = (x + 1)²

y = x² - 3

y = (x + 3)²

y = x² + 2

Select the correct equation which is represented by graph C.

y = x²

y = 2x²

y = 3x²

y = (x - 3)²

y = (x - 2½)²

y = (x + 1)²

y = x² - 3

y = (x + 3)²

y = x² + 2

• Question 1

What shape are these curves?

parabolas
EDDIE SAYS
They are all parabolic. Their equations will have an x² term.
• Question 2

Select the correct equation which is represented by graph B.

y = x²
EDDIE SAYS
This is the basic y = x² curve.
• Question 3

Select the correct equation which is represented by graph C.

y = (x + 1)²
EDDIE SAYS
This is the basic y = x² curve shifted 1 unit to the left.
When x = -1, y = 0.
• Question 4

Select the correct equation which is represented by graph B.

y = x²
EDDIE SAYS
This is the basic y = x² curve.
• Question 5

Select the correct equation which is represented by graph A.

y = x² - 3
EDDIE SAYS
This is the basic y = x² curve shifted down 3 units.
When x = 0, y = -3.
• Question 6

Select the correct equation which is represented by graph A.

y = (x - 2½)²
EDDIE SAYS
This is the basic y = x² curve shifted 2½ units to the right.
When x = 2½, y = 0.
• Question 7

Select the correct equation which is represented by graph A.

y = 2x²
EDDIE SAYS
This is the basic y = x² curve where the x² term has been multiplied by 2.
• Question 8

Select the correct equation which is represented by graph B.

y = (x + 3)²
EDDIE SAYS
This is the basic y = x² curve shifted 3 units to the left.
When x = -3, y = 0.
• Question 9

Select the correct equation which is represented by graph C.

y = 3x²
EDDIE SAYS
This is the basic y = x² curve where the x² term has been multiplied by 3.
• Question 10

Select the correct equation which is represented by graph C.

y = x² + 2
EDDIE SAYS
This is the basic y = x² curve shifted 2 units up.
When x = 0, y = 2.
---- OR ----

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