Concept Check - Writing Quadratic Equations

What is the vertex in: $f\left(x\right)=-2\left(x-6\right)^2+3\ \ \ \$  

• (-6, -3)

• (6, 3)

• (6, -3)

• (-6, 3)

Given a parabola with the vertex (-2, 4) that goes through the point (0,6), calculate 'a.'

• $a=\frac{1}{2}$

• $a=\frac{3}{4}$

• $a=-\frac{1}{2}$

• $a=\frac{5}{2}$

What are the x-intercepts for the parabola:

 $g\left(x\right)=\frac{3}{4}\left(x-3\right)\left(x+12\right)$  

•  $x=\frac{3}{4}$  

•  $x=3\ and\ -12$  

•  $x=-3\ and\ 12$  

• Cannot be determined from that form

Given the x-intercepts of

 $x=-2\ and\ x=6$  and the point  $\left(1,\ 30\right)$ , calculate 'a'.

•  $a=-\frac{30}{7}$  

•  $a=-15$  

•  $a=\frac{35}{3}$  

•  $a=-2$  

Multiply:  $\left(2x+5\right)^2$  

•  $4x^2+25$  

•  $2x^2+10$  

•  $4x^2+20x+25$  

•  $4x^2+14x+25$  

Multiply:  $\left(3x-4\right)\left(x+2\right)$  

•  $3x^2+2x-8$  

•  $3x^2+10x+8$  

•  $3x^2-2x-8$  

•  $3x^2+2x+8$  

Convert  $f\left(x\right)=2\left(x-1\right)^2+6$  into standard form

•  $f\left(x\right)=2x^2-3x+7$  

•  $f\left(x\right)=2x^2-4x+2$  

•  $f\left(x\right)=2x^2-4x+8$  

•  $f\left(x\right)=2x^2-8x+8$  

Convert  $g\left(x\right)=3\left(x+4\right)\left(x+1\right)$  into standard form

•  $g\left(x\right)=3x^2+4x+1$  

•  $g\left(x\right)=3x^2+7x+4$  

•  $g\left(x\right)=3x^2+5x+4$  

•  $g\left(x\right)=3x^2+15x+12$