Foundations Level
Advanced Math
Build a strong foundation in quadratics, exponential functions, and polynomials.
What You'll Learn
Quadratic Equations
Solve quadratic equations using factoring, completing the square, and the quadratic formula.
Exponential Functions
Understand exponential growth and decay, and work with exponential equations.
Basic Polynomials
Add, subtract, multiply polynomials and understand polynomial structure.
Parabolas
Graph quadratic functions and identify key features like vertex and axis of symmetry.
Key Concepts
- •Quadratic Formula: x = (-b ± √(b² - 4ac)) / 2a
- •Factoring: Find two numbers that multiply to c and add to b in x² + bx + c
- •Exponential Growth: y = a(1 + r)ᵗ where r is the growth rate
- •Vertex Form: y = a(x - h)² + k where (h, k) is the vertex
- •FOIL Method: (a + b)(c + d) = ac + ad + bc + bd
Example Problem
Solve for x: x² - 5x + 6 = 0
Solution:
Factor the quadratic: (x - 2)(x - 3) = 0
Set each factor equal to zero:
x - 2 = 0 or x - 3 = 0
x = 2 or x = 3
Study Tips
- ✓Always check if a quadratic can be factored before using the quadratic formula
- ✓When graphing parabolas, identify the vertex, axis of symmetry, and y-intercept
- ✓Remember that exponential functions never touch the x-axis (horizontal asymptote)
- ✓Practice recognizing patterns in polynomial multiplication and factoring
Start Practicing
Ready to test your skills? Choose how you want to study: