4.7 Homework: completing the square

A pizza (a perfect circle) has a 3" radius for the real pizza part (the part with cheese). But they advertise it as having an area of 25 $\pi$ square inches, because they include the crust. How wide is the crust?

According to NBA rules, a basketball court must be precisely 94 feet long and 50 feet wide. (That part is true—the rest I’m making up.) I want to build a court, and of course, bleachers around it. The bleachers will be the same depth (*by “depth” I mean the length from the court to the back of the bleachers) on all four sides. I want the total area of the room to be 8,000 square feet. How deep must the bleachers be?

Recall that the height of a ball thrown up into the air is given by the formula:

$h(t)=h_o+v_{o}t-\text{16}{t}^2$

I am standing on the roof of my house, 20 feet up in the air. I throw a ball up with an initial velocity of 64 feet/sec. You are standing on the ground below me, with your hands 4 feet above the ground. The ball travels up, then falls down, and then you catch it. How long did it spend in the air?

$x^2+\mathrm{6x}+8=0$

$x^2-\text{10}x+3=5$

$x^2+\mathrm{8x}+\text{20}=0$

$x^2+x=0$

${\mathrm{3x}}^2-\text{18}x+\text{12}=0$

Consider the equation $x^2+\mathrm{4x}+4=c$ where $c$ is some constant. For what values of $c$ will this equation have…

• a Two real answers?
• b One real answer?
• c No real answers?

Solve by completing the square: $x^2+\mathrm{6x}+a=0$ . ( $a$ is a constant.)