7A-5 Practice

The quadratic function

 $f\left(x\right)=a\left(x-4\right)^2-1$  passes through the point  $\left(3,\ -6\right).$  What is the value of  $a?$  

The quadratic function  $f\left(x\right)=a\left(x-6\right)^2-1$  passes through the point  $\left(4,\ 0\right).$  What is the value of  $a?$  

Which quadratic function has a vertex of  $\left(-1,\ 5\right)$  and passes through the point  $\left(-4,\ 8\right)?$  

•  $y=\frac{1}{3}\left(x+1\right)^2+5$  

•  $y=3\left(x+1\right)^2+5$  

•  $y=\frac{3}{25}\left(x-1\right)^2+5$  

•  $y=\frac{1}{2}\left(x+1\right)^2+5$  

Which quadratic function has a vertex of $\left(4,\ -3\right)$ and a point at $\left(-2,\ -21\right)?$  

•  $f\left(x\right)=\frac{1}{2}\left(x-4\right)^2-3$  

•  $f\left(x\right)=-\frac{1}{2}\left(x+4\right)^2-3$  

•  $f\left(x\right)=-\frac{1}{2}\left(x-4\right)^2-3$  

•  $f\left(x\right)=\frac{1}{2}\left(x+4\right)^2-3$  

The parent function  $f\left(x\right)=x^2$  is transformed to create  $g\left(x\right)=-\left(x+3\right)^2.$  Which best describes the transformations that occurred?

• A reflection over the y-axis and a shift right

• A reflection over the y-axis and a shift left

• A reflection over the x-axis and a shift right

• A reflection over the x-axis and a shift left

The parent function  $f\left(x\right)=x^2$  is transformed to create  $g\left(x\right)=\frac{1}{4}f\left(x\right).$  Which best describes the change that occurred?

• The graph of g becomes wider than the graph of f.

• The graph of g becomes narrower than the graph of f. 

• The graph of g shifts up higher than the graph of f. 

• The graph of g shifts to the right of the graph of f. 

The parent quadratic function  $f\left(x\right)=x^2$  is transformed to create  $g\left(x\right)=f\left(2x\right)+5.$  Which graph shows this transformation?

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