Quadratics & Exponential

Quadratics & Exponential STAAR PREP

Quadratics

Vertex = middle point

ROXS = x-intercept

Axis of Symmetry = middle point

Fill in the Blanks

What is the maximum value of g? (hint: y-value)

Multiple Choice

Which coordinate best represents the vertex of the graph?

• (2.4, 0)

• (0, -1)

• (-0.4, 0)

• (1, -2)

Multiple Choice

Which statements are best supported by the graph of k?

• I and II only

• I and III only

• II and III only

• I, II, and III

Multiple Choice

Which statements are best supported by the graph of k?

• I and II only

• I and III only

• II and III only

• I, II, and III

Multiple Choice

Which function is best represented by the graph of this situation?

• $h\left(t\right)=-16t^2-64t$

• $h\left(t\right)=-16t^2+128t-256$

• $h\left(t\right)=-16t^2+64t$

• $h\left(t\right)=-16t^2-128t-256$

Multiple Choice

Which quadratic function in vertex form can be represented by the graph that has a vertex at (3, -7) and passes through the point (1, -10)?

• $y=\frac{3}{4}\left(x+3\right)^2+7$

• $y=-\frac{3}{4}\left(x+3\right)^2-7$

• $y=\frac{3}{4}\left(x-3\right)^2+7$

• $y=-\frac{3}{4}\left(x-3\right)^2-7$

Fill in the Blanks

What is the positive solution to this equation? 
 $2x^2+12x=80$  

Multiple Choice

What are the solutions to  $\left(x+7\right)^2=81$  ?

• -74 and 88

• -2 and 16

• -88  and 74

• -16 and 2

Multiple Choice

Which statement $f\left(x\right)=2x^2-3x-5$  

is true?

• The zeros are  $-\frac{5}{2}and\ -1,\ because\ f\left(x\right)=\left(x+1\right)\left(2x+5\right).$  

• The zeros are  $-\frac{5}{2}and\ 1,\ because\ f\left(x\right)=\left(x-1\right)\left(2x+5\right).$  

• The zeros are  $-1\ and\ \frac{5}{2},\ because\ f\left(x\right)=\left(x+1\right)\left(2x-5\right).$  

• The zeros are  $1\ and\ \frac{5}{2},\ because\ f\left(x\right)=\left(x-1\right)\left(2x-5\right).$  

Quadratic transformations

Remember-
parent function :  $f\left(x\right)=x^2$  

Multiple Choice

Which statement about the relationship between the graph of f and the graph of g(x) = 7x² is true?

• The graph of g is narrower than the graph of f

• The graph of g is wider than the graph of f

• the graph g is 7 units below the graph of f

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

Multiple Choice

How did we transform from y=x^2?
y = -3x²

• reflection in x-axis and vertical shift down
• reflection x-axis and vertical stretch
• horizontal stretch
• reflection x-axis and vertical compression

Multiple Choice

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

Multiple Choice

Which expression is a factor of  $18x^2-15x+2$  ?

• 3x - 2

• 9x - 1

• x - 2

• 2x - 1

Multiple Choice

Which expression is a factor of  $x^2-5x-6?$  

• x - 6

• x - 2

• x - 3

• x - 1

Exponential Functions

Growth and Decay

 $f\left(x\right)=a\left(b\right)^x$  

a = initial value (y-int)
b = factor

Fill in the Blanks

What is the value of the y-intercept of the graph of  $g\left(x\right)=245\left(3\right)^x$  

Multiple Choice

Which inequality best represents the domain of the part shown?

• $y\ge4.5$

• $x\ge-2$

• $y\ge-2$

• $x\ge4.5$

Multiple Choice

Which inequality best represents the range of f in this situation?

• $x\ge0$

• $y\ge250,000$

• $0\le x\le110$

• $250,000\le y\le1,000,000$

Multiple Choice

Which statement about the graph of  $y=\ 5\left(0.13\right)^x$  is true?

• The coordinates of the x-intercept are (0.13, 0).

• The coordinates of the y-intercept are (0, 5).

• The equation of the asymptote is x = 0.

• The graph includes the point (2,1).

Multiple Choice

There are 1,024 players in a tennis tournament. In each round, half the players are eliminated. Which function can be used to find the number of players remaining in the tournament at the end of x rounds?

• $f\left(x\right)=1,024\left(1.50\right)^x$

• $f\left(x\right)=1,024\left(0.50\right)^x$

• $f\left(x\right)=1,024\left(1.05\right)^x$

• $f\left(x\right)=1,024\left(0.05\right)^x$

Multiple Choice

You earn annual compound interest with a bank account. The balance in the account after x years can be modeled by  $b\left(x\right)=900\left(1.027\right)^x$  .

Which statement is the best interpretation of one of the values in this function?

• The initial balance of the account decreases at a rate of 97.3% each year.

• The balance in the account increases at a rate of 2.7% each year.

• The initial balance of the account was $1,027.
  

• The balance in the account at the end of one year is $900.