Mr. Alim's science class launched a toy rocket from ground level with an initial upward velocity of 60 feet per second. The height $h$ of the rocket in feet above the ground after $t$ seconds is modeled by the equation $h=60 t-16 t^2$. How long was the rocket in the air before it returned to the ground?

A construction company is planning to pour concrete for a driveway. The length of the driveway is 16 feet longer than its width $w$.

a. Write an expression for the area of the driveway.

b. Find the dimensions of the driveway if it has an area of 260 square feet.

Find the product.

$$\left(2 b^2-g\right)\left(2 b^2+g\right)$$

Find the product.

$$\left(6 b^3-g\right)^2$$

A landscaping company has been commissioned to design a triangular flower bed for a mall entrance. The final dimensions of the flower bed have not been determined, but the company knows that the height will be two feet less than the base. The area of the flower bed can be represented by the equation $A=\frac{1}{2} b^2-b$.

a. Write this equation in factored form.

b. Suppose the base of the flower bed is 16 feet. What will be its area?

Find all values of $k$ so that the trinomial $x^2+k x-35$ can be factored using integers.

Lauren dove into a swimming pool from a 15-foot-high diving board with an initial upward velocity of 8 feet per second. Find the time $t$ in seconds it took Lauren to enter the water. Use the model for vertical motion given by the equation $h=-16 t^2+v t+s$, where $h$ is height in feet, $t$ is time in seconds, $v$ is the initial upward velocity in feet per second, and $s$ is the initial height in feet. (Hint: Let $h=0$ represent the surface of the pool.)

Solve the equation. Check your solutions.

$$8 x^2=-26 x$$

Solve the equation. Check the solutions.

$$17 r+r^2=-52$$

Solve the equation. Check the solutions.

$$18 a^2+10 a=-11 a+4$$

Phenylketonuria (PKU) is a recessive genetic disorder. If both parents are carriers, what is the probability of this couple having a child with PKU? What is the chance of this couple having two children with PKU?

Suppose both parents can roll their tongues but their son cannot. Draw a pedigree showing this trait, and label each symbol with the appropriate genotype.

Construct a family pedigree of two unaffected parents with a child who suffers from cystic fibrosis.

Determine whether the trinomial is a perfect square trinomial. Write yes or no. If so, factor it.

$$g^2-14 g+49$$