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Hotmath Practice Problems

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Title:
Hotmath Algebra 1
Author:
Hotmath Team
Chapter:Quadratic EquationsSection:Graphs of Quadratic Equations
 

Problem: 1

Write the equation of the axis of symmetry, find the vertex, state if the vertex is a maximum or minimum, and graph the equation.

y = 4x2

 

Problem: 3

Write the equation of the axis of symmetry, find the vertex, state if the vertex is a maximum or minimum, and graph the equation.

y = x2 + 2x + 18

 

Problem: 5

Write the equation of the axis of symmetry, find the vertex, state if the vertex is a maximum or minimum, and graph the equation.

y = –x2 + 4x – 1

 

Problem: 7

Write the equation of the axis of symmetry, find the vertex, state if the vertex is a maximum or minimum, and graph the equation.

y = 2x2 + 12x – 11

 

Problem: 9

Write the equation of the axis of symmetry, find the vertex, state if the vertex is a maximum or minimum, and graph the equation.

y = –3x2 – 6x + 4

 

Problem: 11

Write the equation of the axis of symmetry, find the vertex, state if the vertex is a maximum or minimum, and graph the equation.

 

Problem: 13

For the given function, complete the following steps.

a. Find whether the graph of the function opens up or down.

b. Write the coordinates of the vertex.

c. Find an equation of the axis of symmetry.

y = –20x2

 

Problem: 15

For the given function, complete the following steps.

a. Find whether the graph of the function opens up or down.

b. Write the coordinates of the vertex.

c. Find an equation of the axis of symmetry.

y = 3x2 – 8x

 

Problem: 17

For the given function, complete the following steps.

a. Find whether the graph of the function opens up or down.

b. Write the coordinates of the vertex.

c. Find an equation of the axis of symmetry.

y = –8x2 + 10x

 

Problem: 19

For the given function, complete the following steps.

a. Find whether the graph of the function opens up or down.

b. Write the coordinates of the vertex.

c. Find an equation of the axis of symmetry.

y = 3x2 + 12x + 5

 

Problem: 21

For the given function, complete the following steps.

a. Find whether the graph of the function opens up or down.

b. Write the coordinates of the vertex.

c. Find an equation of the axis of symmetry.

y = 4x2 – 5x – 4

 

Problem: 23

For the given function, complete the following steps.

a. Find whether the graph of the function opens up or down.

b. Write the coordinates of the vertex.

c. Find an equation of the axis of symmetry.

y = –2x2 + 4x + 20

 

Problem: 25

Graph the function y = 2x2 + 4x – 1 and mark the coordinates of the vertex.

 

Problem: 27

Graph the function y = 6x2 – 3x – 2 and mark the coordinates of the vertex.

 

Problem: 29

Graph the function y = –8x2 + 8x + 3 and mark the coordinates of the vertex.

 

Problem: 31

Find the equation of the axis of symmetry along with the coordinates of the vertex of the graph for the following equation. Find whether the vertex is a maximum or minimum, and then graph the equation.

y = –2x2 – 4x + 8

 

Problem: 33

Find the equation of the axis of symmetry along with the coordinates of the vertex of the graph for the following equation. Find whether the vertex is a maximum or minimum and then graph the equation.

y = 2(x + 1)2 – 16

 

Problem: 35

Find the equation of the axis of symmetry along with the coordinates of the vertex of the graph for the following equation. Find whether the vertex is a maximum or minimum and then graph the equation.

 

Problem: 37

Graph the equation.

y + 3 = x2 – 8x + 18

 

Problem: 39

Graph the equation.

y + 2 = –3(x – 2)2

 

Problem: 41

Given the x–intercepts –5 and 3, find the equation of the axis of symmetry of a parabola.