<< Chapter < Page Chapter >> Page >

Find two consecutive even numbers whose product is 624.

Got questions? Get instant answers now!

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.

The height of the banner is 13 cm and the length of the side is 54 cm.

Got questions? Get instant answers now!

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.

Got questions? Get instant answers now!

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.

The image shows a rectangular pathway with a right inlaid in the lower left corner. The right angle of the triangle overlays the lower left corner of the rectangle. The left leg of the right triangle overlays the left side of the rectangle and the hypotenuse of the right triangle runs from the upper left corner of the rectangle to a point on the bottom of the rectangle.

The lengths of the sides of the mosaic are 2.2 and 4.4 feet.

Got questions? Get instant answers now!

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.

Got questions? Get instant answers now!

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.

The width of the front walk is 8.1 feet and its length is 30.8 feet.

Got questions? Get instant answers now!

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.

The image shows four rectangular tables placed side by side to create one large table.
Got questions? Get instant answers now!

A ball is thrown vertically in the air with a velocity of 160 ft/sec. Use the formula h = −16 t 2 + v 0 t to determine when the ball will be 384 feet from the ground. Round to the nearest tenth.

The ball will reach 384 feet on its way up in 4 seconds and on the way down in 6 seconds.

Got questions? Get instant answers now!

A bullet is fired straight up from the ground at a velocity of 320 ft/sec. Use the formula h = −16 t 2 + v 0 t to determine when the bullet will reach 800 feet. Round to the nearest tenth.

Got questions? Get instant answers now!

10.5 Graphing Quadratic Equations in Two Variables

In the following exercises, graph by plotting point.

In the following exercises, determine if the following parabolas open up or down.

y = −3 x 2 + 3 x 1

down

Got questions? Get instant answers now!

y = −4 x 2 7 x + 1

Got questions? Get instant answers now!

In the following exercises, find the axis of symmetry and the vertex.

y = x 2 + 6 x + 8

x = 3 ( 3 , 17 )

Got questions? Get instant answers now!

In the following exercises, find the x - and y -intercepts.

y = x 2 4 x + 5

y : ( 0 , 5 ) ; x : ( 5 , 0 ) , ( −1 , 0 )

Got questions? Get instant answers now!

y = x 2 4 x + 10

y : ( 0 , 10 ) ; x : none

Got questions? Get instant answers now!

y = −5 x 2 30 x 46

Got questions? Get instant answers now!

y = 16 x 2 8 x + 1

y : ( 0 , 1 ) ; x : ( 1 4 , 0 )

Got questions? Get instant answers now!

In the following exercises, graph by using intercepts, the vertex, and the axis of symmetry.

y = x 2 + 8 x + 15

y : ( 0 , 15 ) ; x : ( −3 , 0 ) , ( −5 , 0 ) ;
axis: x = −4 ; vertex : ( −4 , −1 )
This figure shows an upward-opening parabola graphed on the x y-coordinate plane. The x-axis of the plane runs from -10 to 10. The y-axis of the plane runs from -2 to 17. The parabola has points plotted at the vertex (-4, -1) and the intercepts (-3, 0), (-5, 0) and (0, 15). Also on the graph is a dashed vertical line representing the axis of symmetry. The line goes through the vertex at x equals -4.

Got questions? Get instant answers now!

y = x 2 + 8 x 16

y : ( 0 , −16 ) ; x : ( 4 , 0 ) ;
axis: x = 4 ; vertex : ( 4 , 0 )
This figure shows a downward-opening parabola graphed on the x y-coordinate plane. The x-axis of the plane runs from -15 to 12. The y-axis of the plane runs from -20 to 2. The parabola has points plotted at the vertex (4, 0) and the intercept (0, -16). Also on the graph is a dashed vertical line representing the axis of symmetry. The line goes through the vertex at x equals 4.

Got questions? Get instant answers now!

y = x 2 + 6 x + 13

y : ( 0 , 13 ) ; x : none ;
axis: x = −3 ; vertex : ( −3 , 4 )
This figure shows an upward-opening parabola graphed on the x y-coordinate plane. The x-axis of the plane runs from -10 to 10. The y-axis of the plane runs from -2 to 18. The parabola has points plotted at the vertex (-3, 4) and the intercept (0, 13). Also on the graph is a dashed vertical line representing the axis of symmetry. The line goes through the vertex at x equals -3.

Got questions? Get instant answers now!

y = −2 x 2 8 x 12

Got questions? Get instant answers now!

y = −4 x 2 + 16 x 11

y : ( 0 , −11 ) x : ( 3.1 , 0 ) , ( 0.9 , 0 ) ;
axis: x = 2 ; vertex: ( 2 , 5 )
This figure shows a downward-opening parabola graphed on the x y-coordinate plane. The x-axis of the plane runs from -10 to 10. The y-axis of the plane runs from -10 to 10. The parabola has points plotted at the vertex (2, 5) and the intercepts (3.1, 0) and (0.9, 0). Also on the graph is a dashed vertical line representing the axis of symmetry. The line goes through the vertex at x equals 2.

Got questions? Get instant answers now!

In the following exercises, find the minimum or maximum value.

y = 7 x 2 + 14 x + 6

The minimum value is −1 when x = −1 .

Got questions? Get instant answers now!

y = −3 x 2 + 12 x 10

Got questions? Get instant answers now!

In the following exercises, solve. Rounding answers to the nearest tenth.

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

In 3.5 seconds the ball is at its maximum height of 196 feet.

Got questions? Get instant answers now!

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 = −2 x 2 + 180 x 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.

Got questions? Get instant answers now!

Practice test

Use the Square Root Property to solve the quadratic equation: 3 ( w + 5 ) 2 = 27 .

w = −2 , −8

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

m = 1 , 3 2

Got questions? Get instant answers now!

Solve the following quadratic equations. Use any method.

3 n 2 + 8 n + 3 = 0

n = −4 ± 7 3

Got questions? Get instant answers now!

x ( x + 3 ) + 12 = 0

no real solution

Got questions? Get instant answers now!

Use the discriminant to determine the number of solutions of each quadratic equation.

6 p 2 13 p + 7 = 0

2

Got questions? Get instant answers now!

Solve by factoring, the Square Root Property, or the Quadratic Formula.

Find two consecutive even numbers whose product is 360.

Two consecutive even number are −20 and −18 and 18 and 20.

Got questions? Get instant answers now!

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.)

Got questions? Get instant answers now!

For each parabola, find which ways it opens, the axis of symmetry, the vertex, the x - and y -intercepts, and the maximum or minimum value.

y = 3 x 2 + 6 x + 8

up x = −1 ( −1 , 5 ) y : ( 0 , 8 ) ; x : none minimum value of 5 when x = −1

Got questions? Get instant answers now!

y = x 2 + 10 x + 24

up x = −5 ( −5 , −1 ) y ; ( 0 , 24 ) ; x : ( −6 , 0 ) , ( −4 , 0 ) minimum value of −5 when x = −1

Got questions? Get instant answers now!

y = −3 x 2 + 12 x 8

Got questions? Get instant answers now!

y = x 2 8 x + 16

down x = −4
( −4 , 32 ) y ; ( 0 , 16 ) ; x : ( −9.7 , 0 ) , ( 1.7 , 0 )
maximum value of 32 when x = −4

Got questions? Get instant answers now!

Graph the following parabolas by using intercepts, the vertex, and the axis of symmetry.

y = 16 x 2 + 24 x + 9

y : ( 0 , 9 ) ; x : ( 3 4 , 0 ) ;
axis: x = 3 4 ; vertex : ( 3 4 , 0 )
This figure shows an upward-opening parabola graphed on the x y-coordinate plane. The x-axis of the plane runs from -10 to 10. The y-axis of the plane runs from -10 to 10. The parabola has points plotted at the vertex (3 fourths, 0) and the intercept (0, 9). Also on the graph is a dashed vertical line representing the axis of symmetry. The line goes through the vertex at x equals 3 fourths.

Got questions? Get instant answers now!

Solve.

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

Got questions? Get instant answers now!
Practice Key Terms 6

Get the best Elementary algebra course in your pocket!





Source:  OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Elementary algebra' conversation and receive update notifications?

Ask