Quadratic Functions

Quadratic Functions

A Review

Multiple Choice

Which of the following is a quadratic function?

• $f\left(x\right)=\left(x-2\right)\left(x+5\right)$

• $f\left(x\right)=\frac{x^2-9}{2x}$

• $f\left(x\right)=2x-5$

• $f\left(x\right)=1+2x-x^2-x^3$

Multiple Choice

The graph of a quadratic function is called a _________

• circle

• hyperbola

• line

• parabola

Multiple Choice

A point on the graph of a quadratic function that is either the highest or the lowest point of the graph.

• focus

• origin

• intercepts

• vertex

Multiple Choice

It is a line that divides the parabola into two parts that are mirror images of each other.

• asymptote

• axis of symmetry

• line of sight

• y-axis

Multiple Choice

A parabola always intersects the x-axis. This statement is ____

• Always True

• Sometimes true

• False

• Neither true nor false

Multiple Choice

Which function below has the narrowest graph?

• $f\left(x\right)=x^2+5$

• $f\left(x\right)=-x^2+2x-5$

• $f\left(x\right)=-2x^2-4x+1$

• $f\left(x\right)=\frac{1}{2}x^2+x-3$

Multiple Choice

What is the vertex form of the quadratic function

 $f\left(x\right)=x^2+4x+7$  ?

•  $f\left(x\right)=\left(x+2\right)^2+3$  

•  $f\left(x\right)=\left(x-2\right)^2+3$  

•  $f\left(x\right)=\left(x+4\right)^2-9$  

•  $f\left(x\right)=\left(x+2\right)^2+11$  

Multiple Choice

Write the quadratic function

 $f\left(x\right)=-2\left(x+1\right)^2+4$  to the the form  $f\left(x\right)=ax^2+bx+c$  

•  $f\left(x\right)=-2x^2+4x+6$  

•  $f\left(x\right)=-2x^2-4x$  

•  $f\left(x\right)=-2x^2-4x+2$  

•  $f\left(x\right)=-2x^2-2x+2$  

Multiple Choice

The following are quadratic inequalities, except:

•  $x^2+2x-5<0$  

•  $\frac{x-5}{2x}>x$  

•  $\frac{3x^2+1}{2}\ge-x$  

•  $x^2+5\ge3x$  

Multiple Choice

Which of the following is the solution of the quadratic inequality   $x^2-9x+20\le0$  ?

•  $x=-5\ and\ x=-4$  

•  $x=5\ and\ x=4$  

•  $4\le x\le5$  

•  $-5\le x\le-4$  

•  $x\le-5\ or\ x\ge-4$  

Multiple Choice

Which of the following is the graph of the quadratic function

 $y=\left(x+3\right)^2-1$  ?

Multiple Choice

If the graph of

 $y=-2x^2$  is shifted 3 units upward and 4 units to the left, the resulting graph is the graph of which function?

•  $y=-2\left(x+3\right)^2-4$  

•  $y=-2\left(x-4\right)^2+3$  

•  $y=-2\left(x-3\right)^2+4$  

•  $y=-2\left(x+4\right)^2+3$  

Multiple Choice

Which quadratic function is represented by the the table of values?

• $y=x^2+2x-3$

• $y=x^2-3x-3$

• $y=x^2-5x-3$

• $y=x^2+x-3$

Multiple Choice

What are the zeroes of the function

 $f\left(x\right)=x^2+8x+7$  ?

• 1 and 7

• -1 and 7

• -1 and -7

• the function has no zeroes

Multiple Choice

What is the equation of the axis of symmetry of the parabola

 $f\left(x\right)=x^2+6x-1$  ?

•  $x=6$  

•  $x=-6$  

•  $x=3$  

•  $x=-3$  

Multiple Choice

What is the vertex of the quadratic function

 $f\left(x\right)=2\left(x-2\right)^2+4$  ?

• (-4, 4)

• (2, 4)

• (-2, 4)

• (4, -2)

Multiple Choice

What is the range of the function

 $f\left(x\right)=-x^2-6x+5$  ?

•  $y\ge-22$  

•  $y\le14$  

•  $y\le-14$  

•  $y\le-4$  

Multiple Choice

What is the direction of the opening of the graph of

 $y=5+2x-2x^2$  ?

• left

• right

• upward

• downward

Multiple Choice

Which function has a vertex of (-3, 4) and contains the point (-1, 5)?

• $y=x^2+6x+13$

• $y=x^2-6x+13$

• $y=2x^2+6x-2$

• $y=x^2+2x-4$