10.5 Graphing quadratic equations  (Page 9/15)

Find two consecutive even numbers whose product is 624.

A triangular banner has an area of 351 square centimeters. The length of the base is two centimeters longer than four times the height. Find the height and length of the base.

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 tile mosaic in the shape of a right triangle is used as the corner of a rectangular pathway. The hypotenuse of the mosaic is 5 feet. One side of the mosaic is twice as long as the other side. What are the lengths of the sides? Round to the nearest tenth.

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.

The front walk from the street to Pam’s house has an area of 250 square feet. Its length is two less than four times its width. Find the length and width of the sidewalk. Round to the nearest tenth.

For Sophia’s graduation party, several tables of the same width will be arranged end to end to give a 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.

A ball is thrown vertically in the air with a velocity of 160 ft/sec. Use the formula $h=\mathrm{-16}{t}^2+v_{0}t$ to determine when the ball will be 384 feet from the ground. Round to the nearest tenth.

A bullet is fired straight up from the ground at a velocity of 320 ft/sec. Use the formula $h=\mathrm{-16}{t}^2+v_{0}t$ to determine when the bullet will reach 800 feet. Round to the nearest tenth.

Graph $y=x^2-2$

Graph $y=\text{−}{x}^2+3$

$y=\mathrm{-3}{x}^2+3x-1$

$y=5x^2+6x+3$

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

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

$y=\text{−}{x}^2+6x+8$

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

$y=x^2-4x+5$

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

$y=x^2-4x+10$

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

$y=16x^2-8x+1$

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

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

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

$y=\text{−}{x}^2+8x-16$

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

$y=x^2+6x+13$

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

$y=\mathrm{-4}{x}^2+16x-11$

$y=x^2+8x+10$

$y=7x^2+14x+6$

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

A ball is thrown upward from the ground with an initial velocity of 112 ft/sec. Use the quadratic equation $h=\mathrm{-16}{t}^2+112t$ to find how long it will take the ball to reach maximum height, and then find the maximum height.

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 $A=\mathrm{-2}{x}^2+180x$ 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.

Use the Square Root Property to solve the quadratic equation: $3{\left(w+5\right)}^2=27$ .

Use Completing the Square to solve the quadratic equation: $a^2-8a+7=23$ .

Use the Quadratic Formula to solve the quadratic equation: $2m^2-5m+3=0$ .

$8v^2+3=35$

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

$2b^2+6b-8=0$

$x\left(x+3\right)+12=0$

$\frac{4}{3}{y}^2-4y+3=0$

$6p^2-13p+7=0$

$3q^2-10q+12=0$

Find two consecutive even numbers whose product is 360.

The length of a diagonal of a rectangle is three more than the width. The length of the rectangle is three times the width. Find the length of the diagonal. (Round to the nearest tenth.)

$y=3x^2+6x+8$

$y=x^2-4$

$y=x^2+10x+24$

$y=\mathrm{-3}{x}^2+12x-8$

$y=\text{−}{x}^2-8x+16$

$y=2x^2+6x+2$

$y=16x^2+24x+9$

A water balloon is launched upward at the rate of 86 ft/sec. Using the formula $h=\mathrm{-16}{t}^2+86t$ , find how long it will take the balloon to reach the maximum height and then find the maximum height. Round to the nearest tenth.