unit 2 math project 16 questions

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Mathematics

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Unit 2 Project- please show work and make it as simple as possible

Complete parts a­bc for each quadratic function.
a. Find the y-­intercept, the equation of the axis of symmetry, and the x­-coordinates of the vertex.
b. Make a table of values that includes the vertex. c. Use the information to graph the function.

  1. f(x) = ­3x^2 + 8x
  2. f(x)=2x^2 +7x+1

Determine whether each function has a maximum or minimum value. State the maximum or minimum value of each function.

  1. f(x)=x^2 +6x+9
  2. f(x)=­-x^2+4x
  3. Write a quadratic equation with roots ­-3 and 4 in standard form.

Solve each quadratic equation using the method of your choice. Find exact solutions.

  1. ­1.6x^2 -­3.2x+18=0
  2. 10x^2 +3x=1
  3. x^2 +8x­-48=0

Simplify the expression.

  1. (5- ­ 2i) -­ (8 ­ -11i)
  2. (14- ­ 5i)^2

Write each equation in vertex form. Then identify the vertex, axis of symmetry, and direction of opening.

  1. y=x^2 +10x+27
  2. y=­9x^2 +54x­8

Graph each inequality.

13. (x­-5)(x+7)<0

14. -­5x^2 +x+2<0

Find the exact solution to the system of equations. Check your answer algebraically.

  1. y=x^2 ­6x+1, y + 2x = 6
  2. 2x^2 ­4x=y+1, x+y=1

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Explanation & Answer

Attached.

Running head: MATHEMATICS QUESTIONS

1

Your name
Instructor’s name
Course
Date of submission

Running head: MATHEMATICS QUESTIONS

2

a. Find the y-intercept, the equation of the axis of symmetry, and the x-coordinates of
the vertex.
1. f(x) = 3x^2 + 8x
Y-intercept = (0, y)
So f(x) = 0
Equation of the axis of symmetry
x= -b/2a
x- Coordinate
x= -b/2a
= -8/6 = -4/3
x coordinate = -4/3
2. f(x)=2x^2 +7x+1
y- Intercept = (0, y)
f( x) =1
Equation of the axis of symmetry
x= -b/2a
x -coordinate
x= -b/2a
x= -7/4
x- coordinate = -7/4
b. Make a table of values that includes the vertex.

x

0

1

2

f(x)=3x2 + 8x

0

11

f(x) =2...


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