Wayground logo

Free Printable Worksheets

Font size

S
M
L
XL
Worksheets

Alg STAAR Quadratic Transformations A.7(C)

Total questions: 15

Worksheet time: 9mins

Name
Class
Date
1.

The graph of f(x)=x2f\left(x\right)=x^2 is reflected over the x-axis and is stretched horizontally to create the graph of function, g. Which graph could represent g?

a)
b)
c)
d)
2.

The graph of f(x)=x2f\left(x\right)=x^2 was translated 4.5 unites to the let to create the graph of function g. Which function represents g?

a)

g(x)=(x−4.5)2g\left(x\right)=\left(x-4.5\right)^2  

b)

g(x)=(x+4.5)2g\left(x\right)=\left(x+4.5\right)^2  

c)

g(x)=x2−4.5g\left(x\right)=x^2-4.5  

d)

g(x)=x2+4.5g\left(x\right)=x^2+4.5  

3.

The graph of quadratic parent function f was transformed to create the graph of g(x)=f(x+2)−5g\left(x\right)=f\left(x+2\right)-5  

a)
b)
c)
d)
4.

The graph of f(x)=x2f\left(x\right)=x^2 was transformed to create the graph of g(x)=f(x)−9g\left(x\right)=f\left(x\right)-9 . Which statement about the graphs is true?

a)

The graph of g is a reflection of the graph of f across the x-axis.

b)

The vertex of the graph of g is 9 unites to the right of the vertex of graph of f.

c)

The graph of g is a reflection of the graph of f across the y-axis.

d)

The y-intercept of the graph of g is 9 unites below the y-intercept of the graph of f.

5.

The graph of quadratic function p is shown on the grid.

If k(x)=x2k\left(x\right)=x^2 and p(x)=k(x)+np\left(x\right)=k\left(x\right)+n , what is the value of n ? Record your answer as an integer (this means it CAN be a negative or positive number but no decimals).

(a)  

6.

The graph of g(x)=x2g\left(x\right)=x^2 was transformed to create the graph of h(x)=−(x4)2h\left(x\right)=-\left(\frac{x}{4}\right)^2  . Which of these describes the transformation from the graph of g to the graph of h?

a)

A reflection over the x-axis and a horizontal stretch

b)

A reflection over the y-axis and a horizontal stretch

c)

A reflection over the x-axis and a vertical stretch

d)

A reflection over the y-axis and a vertical stretch

7.

The graph of f(x)=x2f\left(x\right)=x^2 was transformed to create the graph of g(x)=(x−7.5)2g\left(x\right)=\left(x-7.5\right)^2 . Which of these describes this transformation?

a)

A horizontal shift to the right 7.5 units

b)

A horizontal shift to the left 7.5 units

c)

A vertical shift down 56.25 units

d)

A vertical shift up 56.25 units

8.

The graph of f(x)=x2f\left(x\right)=x^2  is transformed to create the graph of h(x)=2f(x)h\left(x\right)=2f\left(x\right)  . Which graph best represents f and h ?

a)
b)
c)
d)
9.

Function p is in the form of y=ax2+cy=ax^2+c . If the values of a and c are both less than 0, which graph could represent p ?

a)
b)
c)
d)
10.

The graph of f(x)=x2f\left(x\right)=x^2   is shown on the grid. Which statement about the relationship between the graph of f and the graph of g(x)=7x2g\left(x\right)=7x^2   is true?

a)

The graph of g is narrower then the graph of f.

b)

The graph of g is wider then the graph of f.

c)

The graph of g is 7 units below the graph of f.

d)

The graph of g is 7 units above the graph of f.

11.

Quadratic functions q and w are graphed on the same coordinate grid. The vertex of graph of q is 18 units below the vertex of graph of w. Which pair of functions could have been used to create the graphs of q and w?

a)

q(x)=18x2q\left(x\right)=18x^2 and w(x)=x2w\left(x\right)=x^2  

b)

q(x)=x2+18q\left(x\right)=x^2+18 and w(x)=x2w\left(x\right)=x^2  

c)

q(x)=−18x2q\left(x\right)=-18x^2 and w(x)=x2w\left(x\right)=x^2  

d)

q(x)=x2−18q\left(x\right)=x^2-18 and w(x)=x2w\left(x\right)=x^2  

12.

The quadratic function f(x)=x2f\left(x\right)=x^2 with vertex (0,0)\left(0,0\right) has been transformed to create g(x)=f(x+8.7)g\left(x\right)=f\left(x+8.7\right) . What is the vertex of gg ?

a)

(0,8.7)\left(0,8.7\right)

b)

(0,−8.7)\left(0,-8.7\right)

c)

(8.7,0)\left(8.7,0\right)

d)

(−8.7,0)\left(-8.7,0\right)

13.

The quadratic function f(x)=x2f\left(x\right)=x^2 is transformed to create the function g(x)=f(x−6)+2g\left(x\right)=f\left(x-6\right)+2 . Choose the correct answer from each drop-down menu to complete the sentence.

The graph of ff is translated 6 units ​ (a)   and 2 units ​ (b)   to create the graph of function gg .

Choose from the below words
right
left
up
down
14.

The quadratic function f(x)=x2f\left(x\right)=x^2 is transformed to create gg as shown in the graph. What is the equation for gg ?

a)

g(x)=f(x+3)−2g\left(x\right)=f\left(x+3\right)-2

b)

g(x)=2f(x+3)−2g\left(x\right)=2f\left(x+3\right)-2

c)

g(x)=f(x−3)+2g\left(x\right)=f\left(x-3\right)+2

d)

g(x)=2f(x−3)+2g\left(x\right)=2f\left(x-3\right)+2

15.

If f(x)=x2f\left(x\right)=x^2 and g(x)=f(x+7.2)g\left(x\right)=f\left(x+7.2\right) , what is the vertex of the graph of gg ?

a)

(7.2,0)\left(7.2,0\right)

b)

(−7.2,0)\left(-7.2,0\right)

c)

(0,7.2)\left(0,7.2\right)

d)

(0,−7.2)\left(0,-7.2\right)