Quadratic Functions and Equations Review

What are the x-intercepts of $y=\left(x-6\right)\left(x-9\right)$ ?

•  $6$  and $9$  

•  $-6$  and $-9$  

•  $-6$  and $9$  

•  $6$  and $-9$  

What is the axis of symmetry of $f\left(x\right)=2\left(x+6\right)^2-3$ ?

•  $x=2$  

•  $x=-3$  

•  $x=-6$  

•  $x=6$  

What is the quadratic function in vertex form for the parabola shown?

•  $f\left(x\right)=-8\left(x-2\right)^2+1$  

•  $f\left(x\right)=-8\left(x-2\right)^2+2$  

•  $f\left(x\right)=8\left(x+1\right)^2+1$  

•  $f\left(x\right)=8\left(x-1\right)^2-2$  

What is the vertex of $y=7\left(x+5\right)^2+4$ ?

•  $\left(5,\ 4\right)$  

•  $\left(-4,5\right)$  

•  $\left(-5,4\right)$  

•  $\left(7,-4\right)$  

Which graph represents the quadratic function $y=\frac{5}{7}\left(x-4\right)^2-7$ ?

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What are the domain and range of $y=7\left(x-1\right)^2-9$ ?

• Domain:  $\left\{x\parallel x\le1,\ x\epsilon R\right\}$  
  Range:  $\left\{y\parallel y\epsilon R\right\}$  

• Domain:  $\left\{x\parallel x\epsilon R\right\}$  
  Range:  $\left\{y\parallel y\ge-9,\ y\epsilon R\right\}$  

• Domain:  $\left\{x\parallel x\ge7,\ x\epsilon R\right\}$  
  Range:  $\left\{y\parallel\ y\epsilon R\right\}$  

• Domain:  $\left\{x\parallel x\epsilon R\right\}$  
  Range:  $\left\{y\parallel y\le-1,\ y\epsilon R\right\}$  

The vertex of a parabola is located at $\left(-5,6\right)$ . If the parabola has a y-intercept of 231, which quadratic function represents the parabola? 

•  $f\left(x\right)=9\left(x-5\right)^2+6$  

•  $f\left(x\right)=9\left(x+5\right)^2+6$  

•  $f\left(x\right)=-9\left(x+5\right)^2+6$  

•  $f\left(x\right)=9\left(x-5\right)^2-6$  

What information can be determined from the quadratic funciton $f\left(x\right)=\frac{2}{3}\left(x+2\right)^2-9$ ?

• The vertex is at $\left(-2,-9\right)$ and the graph opens upward

• The vertex is at $\left(-9,-2\right)$ and the graph opens downward

• The vertex is at $\left(-2,-9\right)$ and the graph opens downward

• The vertex is at $\left(-9,-2\right)$ and the graph opens upward

Which function is not quadratic?

• $f\left(x\right)=\left(6x+9\right)\left(\frac{1}{9}x-9\right)$

• $f\left(x\right)=x\left(x-9\right)\left(6x+8\right)$

• $f\left(x\right)=7x^2+8$

• $f\left(x\right)=6\left(x-9\right)^2$

Identify the characteristics of this graph.

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