2.4 Writing Equations of Quadratics Practice

If asked to write the equation of a parabola that passes through the point (1,12) and has a vertex at (10,-4), which method would you use?

• Vertex form:

  $y=a\left(x-h\right)^2+k$

• Desmos: $y=ax^2+bx+c$

If asked to write the equation of a parabola that passes through the point (1,12) and has a vertex at (10,-4), point would represent (h,k) and which point would represent (x,y)?

• (x,y): (1,12)

• (x,y): (10,-4)

• (h,k): (1,12)

• (h,k): (10,-4)

If asked to write the equation of a parabola that passes through the point (1,12) and has a vertex at (10,-4), find the value of a using vertex form  $y=a\left(x-h\right)^2+k$  

•  $\ a=\frac{16}{81}$ 

•  $a=-\frac{81}{16}$  

•  $a=-\frac{8}{81}$  

•  $a=\frac{81}{8}$  

If asked to write the equation of a parabola that passes through the point (1,12) and has a vertex at (10,-4), use the a value you just found to write the equation of the parabola.

•  $\ y=\frac{16}{81}\left(x-1\right)^2+12$ 

•  $y=\frac{16}{81}\left(x-10\right)^2-4$  

•  $y=\frac{81}{16}\left(x-1\right)^2+12$  

•  $a=\frac{81}{16}\left(x-10\right)^2-4$  

If asked to write the equation of a parabola that passes through the point (0,20) and has a vertex at (80,30), which method would you use?

• Vertex form:

  $y=a\left(x-h\right)^2+k$

• Desmos: $y=ax^2+bx+c$

If asked to write the equation of a parabola that passes through the point (0,20) and has a vertex at (80,30), what point would represent (h,k) and which point would represent (x,y)?

• (h,k): (0,20)

• (h,k): (80,30)
  

• (x,y): (0,20)

• (x,y): (80,30)

If asked to write the equation of a parabola that passes through the point (0,20) and has a vertex at (80,30), find the a-value for the equation. 

•  $a=\frac{4}{5}$  
  

•  $a=-\frac{4}{5}$  
  

•  $a=\frac{1}{640}$  
  

•  $a=-\frac{1}{640}$  
  

Write the equation of a parabola that passes through the point (0,20) and has a vertex at (80,30), using the a-value you found in the previous problem

•  $y=\frac{1}{640}\left(x-80\right)^2+30$  
  

•  $y=-\frac{1}{640}\left(x-30\right)^2+80$  
  

•  $y=\frac{1}{640}\left(x-0\right)^2+20$  
  

•  $y=-\frac{1}{640}\left(x-80\right)^2+30$  
  

If asked to write the equation of a parabola using the table of values above, which method would you use?

• Vertex form:

  $y=a\left(x-h\right)^2+k$

• Desmos:

  $y=ax^2+bx+c$

Use DESMOS to find your a, b and c values.

• a=-16

• a=1

• b=0

• c=150

• c=6.76