SAT1M1-131415

Front

What is the quadratic formula used to solve equations of the form ax² + bx + c = 0?

Back

x = (-b ± √(b² - 4ac)) / (2a)

Front

What does it mean for a function to be quadratic?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax² + bx + c.

Front

How do you determine the number of solutions for a quadratic equation?

Back

By calculating the discriminant (b² - 4ac). If it's positive, there are two solutions; if zero, one solution; if negative, no real solutions.

Front

What is exponential growth?

Back

Exponential growth occurs when the growth rate of a value is proportional to its current value, leading to rapid increases over time.

Front

If a population doubles every 3 hours, how can you express this mathematically?

Back

If P is the initial population, after t hours, the population can be expressed as P(t) = P * 2^(t/3).

Front

What is the initial population of bacteria in the given problem?

Back

300,000 cells per milliliter.

Front

How many times does the population double in 15 hours if it doubles every 3 hours?

Back

The population doubles 5 times in 15 hours (15/3 = 5).

Front

What is the formula to calculate the final population after a certain number of doublings?

Back

Final Population = Initial Population * 2^(number of doublings).

Front

What is the significance of the roots of a quadratic equation?

Back

The roots (or solutions) of a quadratic equation represent the x-values where the graph intersects the x-axis.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point on the graph of a quadratic function, found at x = -b/(2a).