Math 1 EOC Review - Exponential and Quadratic Word Problems

Front

What is the general form of a quadratic function?

Back

The general form of a quadratic function is f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What does the vertex of a parabola represent in a quadratic function?

Back

The vertex of a parabola represents the maximum or minimum point of the quadratic function, depending on the direction of the parabola.

Front

How do you find the x-intercepts of a quadratic function?

Back

To find the x-intercepts, set f(x) = 0 and solve the equation ax² + bx + c = 0 using factoring, completing the square, or the quadratic formula.

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form f(t) = a * b^t, where a is a constant, b is the base (b > 0), and t is the exponent.

Front

What does it mean for a population to be increasing exponentially?

Back

A population is increasing exponentially if it grows by a constant percentage over equal time intervals, leading to rapid growth.

Front

What is the y-intercept of a function?

Back

The y-intercept of a function is the point where the graph intersects the y-axis, which occurs when x = 0.

Front

How do you determine if a quadratic function opens upwards or downwards?

Back

A quadratic function opens upwards if the coefficient 'a' is positive and downwards if 'a' is negative.

Front

What is the formula for the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of the quadratic equation ax² + bx + c = 0.

Front

What does the term 'initial value' refer to in an exponential function?

Back

The initial value in an exponential function is the value of the function when t = 0, represented by the constant 'a' in f(t) = a * b^t.

Front

How can you model population growth using an exponential function?

Back

Population growth can be modeled using the function P(t) = P0 * e^(rt), where P0 is the initial population, r is the growth rate, and t is time.