Quadratic Word Problems-Zeros/Roots

A quarterback passes a football through the air. The height h of the ball in yards after the distance d in yards the ball travels horizontally is given by $h\left(d\right)=-0.25d^2+2d+6$ . How far horizontally from the quarterback passing the ball will the ball land on the ground if it’s not caught? Round to the nearest yard.

• about 2 yds.

• about 7 yds

• about 6 yds.

• about 10 yds.

You throw a ball upward. Its height, h, in feet, after t seconds can be modeled by the function   $h\left(t\right)=-16t^2+30t+6$  After how many seconds will it hit the ground? Round to the nearest 100th.

• about .18 ft.

• about 32.92 ft.

• about 2.06 ft.

• about 6.02 ft.

An architect designing a rectangular patio wants to place a brick border on the outside with a width of x feet. The inside of the patio without the brick border will have dimensions of 8 feet by 13 feet.

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Together the patio with the border will have an area of 160 square feet. Write an equation that can be used to find x, the width of the brick border, and then solve your equation to the nearest tenth of a foot.

• about 1.2 ft.

• about 5 ft

• about 8.2 ft.

• about 11.7 ft.

Write the function rule in standard form for the following function.

• $y=x^2-2x-24$

• $y=-x^2+2x+24$

• $y=x^2+2x-24$

• $y=-x^2-2x+24$

For the graph of $y=-2x^2+12x–7$ , algebraically find the equation of its axis of symmetry.

•  $x=3$  

•  $x=\frac{1}{3}$  
  

•  $x=-3$  
  

•  $x=-\frac{1}{3}$  

For the graph of $y=-2x^2+12x–7$ , algebraically find the coordinates of its vertex

•  $\left(-3,\ -61\right)$  

•  $\left(\frac{1}{3},\frac{-29}{9}\right)$  

•  $\left(-\frac{1}{3},-\frac{101}{9}\right)$  

•  $\left(3,11\right)$  

For the graph of $y=-2x^2+12x–7$ , write the equation in vertex form.

•  $y=-2\left(x+3\right)^2-61$  

•  $y=-2\left(x+\frac{1}{3}\right)^2+\frac{101}{9}$  

•  $y=-2\left(x-\frac{1}{3}\right)^2-\frac{29}{9}$  

•  $y=-2\left(x-3\right)^2+11$  

A contractor needs 54 square feet of brick to construct a rectangular walkway. The length of the walkway is 15 feet more than the width. Write an equation that could be used to determine the dimensions of the walkway.

• $w+\left(w+15\right)=54$

• $w\left(w+15\right)=54$

• $w\left(w-15\right)=54$

• $w^2+\left(w+15\right)^2=54$

A contractor needs 54 square feet of brick to construct a rectangular walkway. The length of the walkway is 15 feet more than the width. Solve the equation to find the length and width.

• $w=\frac{39}{2}\ ft,\ l=\frac{69}{2}ft.$

• $w=9\ ft,\ l=24\ ft.$

• $w=3\ ft,\ \ l=18\ ft.$

• $w=\ 4\ ft,\ l=9\ ft.$