Ethan Sanchez
MTH 102-1
Ethan Sanchez
Dr. Mary Wright
Algebra Homework Assignment
Solutions Included
Question 1: Solve for x: 3x = 3
Approach:
Step 1: Divide both sides by 3.
x=1
Exercise 2: Find the vertex, axis of symmetry, y-intercept, and x-intercepts (if any) of the
parabola: f(x) = 5x² - 4x - 3
Answer:
Step 1: Find the vertex using the formula x = -b/(2a).
x = --4/(2 × 5) = 0.40
Step 2: Find the y-coordinate of the vertex by substituting x into the function.
f(0.40) = 5(0.40)² - 4(0.40) - 3 = -3.80
Step 3: The vertex is (0.40, -3.80).
Step 4: The axis of symmetry is the vertical line through the vertex.
x = 0.40
Step 5: The y-intercept is found by setting x = 0.
f(0) = 5(0)² - 4(0) - 3 = -3
Step 6: Find the x-intercepts by setting f(x) = 0 and solving for x.
5x² - 4x - 3 = 0
Using the quadratic formula: x = (-b ± √(b² - 4ac))/(2a)
Discriminant = b² - 4ac = -4² - 4 × 5 × -3 = 76
Since the discriminant is positive, there are two real x-intercepts.
x = (4 ± √76)/(2 × 5)
x = 1.2717797887081348 or x = -0.4717797887081348
Step 7: The x-intercepts are x = 1.27 or x = -0.47.
Page 1 of 5
, Ethan Sanchez
Note: Okay, the professor was explaining this in class, but I had to ask an extra question for
more help (I went to tutoring after class)
Problem 3: Solve the quadratic equation: 2x² + 0x - 4 = 0
Solution:
Step 1: Use the quadratic formula.
x = (-b ± √(b² - 4ac)) / 2a
Step 2: Substitute values.
x = (-0 ± √(0² - 4 × 2 × -4)) / (2 × 2)
x = (0 ± √(0 - -32)) / 4
x = (0 ± √32) / 4
Step 3: Calculate the solutions.
x = 1.41 or x = -1.41
Note: I double-checked this approach with the notes from Professor Wright's review
session.
4.: Solve for x: 8x = 32
Work:
Step 1: Divide both sides by 8.
x=4
Note: I started by identifying this as a algebra problem, similar to Example 3.2 in the text.
Follow method discussed in class
5): Solve for x: 6x = 30
Approach:
Step 1: Divide both sides by 6.
x=5
Page 2 of 5
MTH 102-1
Ethan Sanchez
Dr. Mary Wright
Algebra Homework Assignment
Solutions Included
Question 1: Solve for x: 3x = 3
Approach:
Step 1: Divide both sides by 3.
x=1
Exercise 2: Find the vertex, axis of symmetry, y-intercept, and x-intercepts (if any) of the
parabola: f(x) = 5x² - 4x - 3
Answer:
Step 1: Find the vertex using the formula x = -b/(2a).
x = --4/(2 × 5) = 0.40
Step 2: Find the y-coordinate of the vertex by substituting x into the function.
f(0.40) = 5(0.40)² - 4(0.40) - 3 = -3.80
Step 3: The vertex is (0.40, -3.80).
Step 4: The axis of symmetry is the vertical line through the vertex.
x = 0.40
Step 5: The y-intercept is found by setting x = 0.
f(0) = 5(0)² - 4(0) - 3 = -3
Step 6: Find the x-intercepts by setting f(x) = 0 and solving for x.
5x² - 4x - 3 = 0
Using the quadratic formula: x = (-b ± √(b² - 4ac))/(2a)
Discriminant = b² - 4ac = -4² - 4 × 5 × -3 = 76
Since the discriminant is positive, there are two real x-intercepts.
x = (4 ± √76)/(2 × 5)
x = 1.2717797887081348 or x = -0.4717797887081348
Step 7: The x-intercepts are x = 1.27 or x = -0.47.
Page 1 of 5
, Ethan Sanchez
Note: Okay, the professor was explaining this in class, but I had to ask an extra question for
more help (I went to tutoring after class)
Problem 3: Solve the quadratic equation: 2x² + 0x - 4 = 0
Solution:
Step 1: Use the quadratic formula.
x = (-b ± √(b² - 4ac)) / 2a
Step 2: Substitute values.
x = (-0 ± √(0² - 4 × 2 × -4)) / (2 × 2)
x = (0 ± √(0 - -32)) / 4
x = (0 ± √32) / 4
Step 3: Calculate the solutions.
x = 1.41 or x = -1.41
Note: I double-checked this approach with the notes from Professor Wright's review
session.
4.: Solve for x: 8x = 32
Work:
Step 1: Divide both sides by 8.
x=4
Note: I started by identifying this as a algebra problem, similar to Example 3.2 in the text.
Follow method discussed in class
5): Solve for x: 6x = 30
Approach:
Step 1: Divide both sides by 6.
x=5
Page 2 of 5
