Review Exercises

$y^2=144$

$4a^2=100$

$r^2+32=0$

$\frac{2}{3}{w}^2-20=30$

${\left(p-5\right)}^2+3=19$

${\left(x-\frac{1}{4}\right)}^2=\frac{3}{16}$

${\left(n-4\right)}^2-50=150$

$n^2+10n+25=12$

$x^2+22x$

$a^2-3a$

$d^2+14d=\mathrm{-13}$

$m^2+6m=\mathrm{-109}$

$v^2-14v=\mathrm{-31}$

$m^2+10m-4=\mathrm{-13}$

$a^2=3a+8$

$\left(u+8\right)\left(u+4\right)=14$

$3p^2-18p+15=15$

$4y^2-6y=4$

$3c^2+2c=9$

$2x^2+6x=\mathrm{-5}$

$4x^2-5x+1=0$

$r^2-r-42=0$

$4v^2+v-5=0$

$3m^2+8m+2=0$

$6a^2-5a+2=0$

$u\left(u-10\right)+3=0$

$\frac{1}{8}{p}^2-\frac{1}{5}p=-\frac{1}{20}$

$4c^2+4c+1=0$

ⓐ $9x^2-6x+1=0$
ⓑ $3y^2-8y+1=0$
ⓒ $7m^2+12m+4=0$
ⓓ $5n^2-n+1=0$

ⓐ $16r^2-8r+1=0$
ⓑ $5t^2-8t+3=9$
ⓒ $3{\left(c+2\right)}^2=15$

$x^4-14x^2+24=0$

$4x^4-5x^2+1=0$

$x+3\sqrt{x}-28=0$

$x^{\frac{2}{3}}-10x^{\frac{1}{3}}+24=0$

$8x^{\mathrm{-2}}-2x^{\mathrm{-1}}-3=0$

Find two consecutive even numbers whose product is 624.

Julius built a triangular display case for his coin collection. The height of the display case is six inches less than twice the width of the base. The area of the of the back of the case is 70 square inches. Find the height and width of the case.

A rectangular piece of plywood has a diagonal which measures two feet more than the width. The length of the plywood is twice the width. What is the length of the plywood’s diagonal? Round to the nearest tenth.

For Sophia’s graduation party, several tables of the same width will be arranged end to end to give serving table with a total area of 75 square feet. The total length of the tables will be two more than three times the width. Find the length and width of the serving table so Sophia can purchase the correct size tablecloth . Round answer to the nearest tenth.

The couple took a small airplane for a quick flight up to the wine country for a romantic dinner and then returned home. The plane flew a total of 5 hours and each way the trip was 360 miles. If the plane was flying at 150 mph, what was the speed of the wind that affected the plane?

Two handymen can do a home repair in 2 hours if they work together. One of the men takes 3 hours more than the other man to finish the job by himself. How long does it take for each handyman to do the home repair individually?

Graph $y=\text{−}{x}^2+3$

ⓐ $y=x^2+8x-1$
ⓑ $y=\mathrm{-4}{x}^2-7x+1$

$y=2x^2-8x+1$

$y=x^2-8x+15$

$y=\mathrm{-5}{x}^2-30x-46$

$y=x^2+16x+64$

$y=x^2-2x-3$

$y=4x^2-4x+1$

$y=\mathrm{-2}{x}^2-8x-12$

$y=\mathrm{-3}{x}^2+12x-10$

A daycare facility is enclosing a rectangular area along the side of their building for the children to play outdoors. They need to maximize the area using 180 feet of fencing on three sides of the yard. The quadratic equation $A(x)=x\left(90-\frac{x}{2}\right)$ gives the area, A, of the yard for the length, x, of the building that will border the yard. Find the length of the building that should border the yard to maximize the area, and then find the maximum area.

$h\left(x\right)=x^2-3$

$g(x)={\left(x-3\right)}^2$

$f(x)={\left(x+3\right)}^2-2$

$f(x)={\left(x-4\right)}^2-3$

$f(x)=\text{−}{x}^2$

$f\left(x\right)=2x^2-4x-4$

$f\left(x\right)=3x^2-6x-1$

$f\left(x\right)=2x^2+4x+6$

$f\left(x\right)=\mathrm{-3}{x}^2-12x-5$

$x^2-x-6>0$

$\text{−}{x}^2-x+2\ge 0$

$x^2-6x+8<0$

$x^2-6x+4\le 0$

$\text{−}{x}^2+x-6>0$