Graphing Calculator

Evaluate linear, quadratic, and exponential functions at specific points.

Linear: y = mx + b; Quadratic: y = ax^2 + bx + c; Exponential: y = a*b^x
Linear: y = 2x + 3 at x=5 -> y=13; Quadratic: y = x^2 - 4x + 3 at x=2 -> y=-1; Exponential: y = 2*3^x at x=3 -> y=54

How do you read a linear function y = mx + b?

m is slope (rise/run, steepness), b is y-intercept (where line crosses y-axis). Example: y = 2x + 3 -> slope = 2 (goes up 2 for every 1 right), crosses y-axis at 3. Positive slope = line rises, negative = falls, zero = horizontal. At x=0, y=b. At y=0 (x-intercept), x = -b/m. Slope formula: m = (y₂-y₁)/(x₂-x₁).

What is a quadratic function and what is its shape?

Quadratic: y = ax^2 + bx + c forms a parabola (U-shape). a > 0: Opens upward (∪), a < 0: Opens downward (∩). Vertex (turning point) at x = -b/2a. Axis of symmetry: x = -b/2a. y-intercept: c. Example: y = x^2 - 4x + 3 -> vertex at x = 2, opens up, crosses y-axis at 3. Used in: Projectile motion, profit curves, optics.

How does exponential growth differ from linear growth?

Linear (y = mx + b): Constant rate, adds same amount each step (1,2,3,4,5...). Graph is straight line. Exponential (y = abˣ): Grows by multiplying, accelerates over time (1,2,4,8,16...). Graph curves upward. Example: $100 at 10% - Linear: +$10/year (110,120,130). Exponential: x1.1/year (110,121,133). Exponential dominates long-term. Seen in: Viruses, investments, technology.

What are the key features of a graph?

Important features: Intercepts (where crosses axes), Slope (linear: rate of change), Vertex (quadratic: max/min point), Asymptotes (lines curve approaches but never touches), Domain (valid x values), Range (possible y values), Increasing/decreasing intervals. Example: y = x^2 → vertex (0,0), opens up, domain: all x, range: y >= 0. Understanding features helps interpret real-world relationships.