Vertex Form

The height in feet of a rocket launched from the ground can be modeled by the function  $f\left(x\right)=-16x^2+128x,$  where  $x$  is the time in seconds after the rocket is launched. What is the rocket's maximum height?

• 288 feet
  

• 144 feet
  

• 256 feet
  

• 576 feet
  

Two identical rubber balls are dropped from different heights. Ball 1 is dropped from a height of 144 feet, and ball 2 is dropped from a height of 256 feet. Write a function for the height of each ball.

• Ball 1: $h_1\left(t\right)=16t^2-144;$ Ball 2: $h_1\left(t\right)=16t^2-256$
  

• Ball 1: $h_1\left(t\right)=-16t^2-144;$ Ball 2: $h_2\left(t\right)=-16t^2-256$
  

• Ball 1: $h_1\left(t\right)=-16t^2+144$ ; Ball 2: $h_2\left(t\right)=-16t^2+256$
  

• Ball 1: $h_1\left(t\right)=16t^2+144;$ Ball 2: $h_2\left(t\right)=16t^2+256$
  

Two identical rubber balls are dropped from different heights. Ball 1 is dropped from a height of 144 feet, and ball 2 is dropped from a height of 256 feet. Determine when each ball will reach the ground.

• Ball 1 reaches the ground in 12 sec.

  Ball 2 reaches the ground in 16 sec.

• Ball 1 reaches the ground in 2 sec.

  Ball 2 reaches the ground in 3 sec.

• Ball 1 reaches the ground in 3 sec.

  Ball 2 reaches the ground in 4 sec.

• Ball 1 reaches the ground in 4 sec.

  Ball 2 reaches the ground in 5 sec.

Write the function  $f\left(x\right)=7x^2-56x+117$  in vertex form.

•  $f\left(x\right)=7\left(x+4\right)^2+5$  

•  $f\left(x\right)=7\left(x-5\right)^2+4$  

•  $f\left(x\right)=7\left(x+5\right)^2+4$  

•  $f\left(x\right)=7\left(x-4\right)^2+5$  

Identify the vertex, written in standard form  $f(x)=7x^2−56x+117$  

•  $\left(-4,\ 5\right)$  

•  $\left(-5,\ 4\right)$  

•  $\left(5,\ 4\right)$  

•  $\left(4,\ 5\right)$  

Identify the correct graph  $y=x^2+5x+8.$ 

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Tags

CCSS.HSF-IF.C.7A

Identify the vertex  $y=x^2+5x+8.$  

•  $\left(-\frac{3}{2},\frac{7}{4}\right)$  

•  $\left(\frac{3}{4},\frac{7}{4}\right)$  

•  $\left(\frac{5}{2},\frac{7}{4}\right)$  

•  $\left(-\frac{5}{2},\frac{7}{4}\right)$  

Find the vertex  $f\left(x\right)=-2x^2+5x+12.$  

•  $\left(\frac{3}{2},\frac{121}{4}\right)$  

•  $\left(\frac{5}{4},\frac{121}{8}\right)$  

•  $\left(-\frac{5}{4},\frac{121}{8}\right)$  

•  $\left(-\frac{3}{2},\frac{121}{4}\right)$  

Find the axis of symmetry  $f\left(x\right)=-2x^2+5x+12.$  

•  $x=-\frac{3}{2}$  

•  $x=\frac{5}{4}$  

•  $x=\frac{3}{2}$  

•  $x=-\frac{5}{4}$  

Find the y-intercept  $f\left(x\right)=-2x^2+5x+12$  

•  $4$  

•  $2$  

•  $12$  

•  $5$  

Tags

CCSS.HSF-IF.C.7A