Parabola of the Form y=x²+c - Examples, Exercises and Solutions

Question Types:
Parabola of the Form y=x²+c: Linking function properties to its representationParabola of the Form y=x²+c: Finding Increasing or Decreasing DomainsParabola of the Form y=x²+c: Identify positive and negative domains on a graphParabola of the Form y=x²+c: Match functions to the appropriate graphsParabola of the Form y=x²+c: Finding points on the graph of a function

Family of Parabolas y=x2+c y=x²+c : Vertical Shift

The basic quadratic function y=x2y=x^2 with the addition of CC yields the function y=x2+cy=x^2+c
The meaning of CC is the vertical shift of the function upwards or downwards.
If CC is positive: the function will rise by the number of steps shown in CC.
If CC is negative: the function will descend by the number of steps shown in CC. 

Detailed explanation

Suggested Topics to Practice in Advance

  1. The functions y=x²

Practice Parabola of the Form y=x²+c

Question 1

Find the ascending area of the function

\( f(x)=2x^2 \)

Question 2

Find the descending area of the function

\( f(x)=\frac{1}{2}x^2 \)

Question 3

One function

\( y=-2x^2-3 \)

to the corresponding graph:

333333-3-3-3333-3-3-3-3-3-31234

Question 4

One function

\( y=6x^2 \)

to the corresponding graph:

1234

Question 5

One function

\( y=-6x^2 \)

to the corresponding graph:

1234

Examples with solutions for Parabola of the Form y=x²+c

Exercise #1

Find the ascending area of the function

f(x)=2x2 f(x)=2x^2

Video Solution

Answer

0 < x

Exercise #2

Find the descending area of the function

f(x)=12x2 f(x)=\frac{1}{2}x^2

Video Solution

Answer

x < 0

Exercise #3

One function

y=−2x2−3 y=-2x^2-3

to the corresponding graph:

333333-3-3-3333-3-3-3-3-3-31234

Video Solution

Answer

4

Exercise #4

One function

y=6x2 y=6x^2

to the corresponding graph:

1234

Video Solution

Answer

2

Exercise #5

One function

y=−6x2 y=-6x^2

to the corresponding graph:

1234

Video Solution

Answer

4

Question 1

Which chart represents the function \( y=x^2-9 \)?

222333999-9-9-9-1-1-1444-101234

Question 2

Find the corresponding algebraic representation for the function

111

Question 3

Find the corresponding algebraic representation for the function

-6-6-6

Question 4

One function

\( y=-\frac{1}{2}x^2+4 \)

to the corresponding graph:

444-4-4-44444441234

Question 5

One function

\( y=\frac{x^2}{4}+2 \)

to the corresponding graph:

4442221234

Exercise #6

Which chart represents the function y=x2−9 y=x^2-9 ?

222333999-9-9-9-1-1-1444-101234

Video Solution

Answer

4

Exercise #7

Find the corresponding algebraic representation for the function

111

Video Solution

Answer

y=−x2+1 y=-x^2+1

Exercise #8

Find the corresponding algebraic representation for the function

-6-6-6

Video Solution

Answer

y=x2−6 y=x^2-6

Exercise #9

One function

y=−12x2+4 y=-\frac{1}{2}x^2+4

to the corresponding graph:

444-4-4-44444441234

Video Solution

Answer

1

Exercise #10

One function

y=x24+2 y=\frac{x^2}{4}+2

to the corresponding graph:

4442221234

Video Solution

Answer

1

Question 1

One function

\( y=x^2+9 \)

to the corresponding graph:

999-9-9-9999-9-9-91234

Question 2

Choose the increasing and decreasing domains of the following function:

\( f(x)=-2x^2+10 \)

Question 3

Find the ascending area of the function

\( f(x)=-3x^2+12 \)

Question 4

Find the ascending area of the function

\( f(x)=-4x^2-24 \)

Question 5

Find the ascending area of the function

\( f(x)=6x^2-12 \)

Exercise #11

One function

y=x2+9 y=x^2+9

to the corresponding graph:

999-9-9-9999-9-9-91234

Video Solution

Answer

3

Exercise #12

Choose the increasing and decreasing domains of the following function:

f(x)=−2x2+10 f(x)=-2x^2+10

Video Solution

Answer

0 < x decreasing

x < 0 increasing

Exercise #13

Find the ascending area of the function

f(x)=−3x2+12 f(x)=-3x^2+12

Video Solution

Answer

x < 0

Exercise #14

Find the ascending area of the function

f(x)=−4x2−24 f(x)=-4x^2-24

Video Solution

Answer

x < 0

Exercise #15

Find the ascending area of the function

f(x)=6x2−12 f(x)=6x^2-12

Video Solution

Answer

0 < x

Topics learned in later sections

  1. Families of Parabolas
  2. Family of Parabolas y=(x-p)²
  3. Family of Parabolas y=(x-p)²+k (combination of horizontal and vertical shifts)