SAT Math: Passport to Advanced Math

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

How do you find the maximum height of a projectile modeled by a quadratic function?

Back

The maximum height can be found using the vertex formula, h = -b/(2a), where h is the time at which the maximum height occurs.

Front

What does the variable 't' represent in the function h = -0.5t² + 8t + 10?

Back

In this function, 't' represents the time in seconds after the rocket is launched.

Front

What is the significance of the coefficient of t² in a quadratic function?

Back

The coefficient of t² determines the direction of the parabola: if it is positive, the parabola opens upwards; if negative, it opens downwards.

Front

How do you solve a quadratic equation using factoring?

Back

To solve a quadratic equation by factoring, express it in the form (x - p)(x - q) = 0, then set each factor to zero: x - p = 0 or x - q = 0.

Front

What are the roots of the equation x² + 2x - 15 = 0?

Back

The roots are x = -5 and x = 3.

Front

What is function composition?

Back

Function composition is the process of applying one function to the results of another function, denoted as f(g(x)).

Front

How do you evaluate f(g(6)) for f(x) = 2x² - 10 and g(x) = 4 - 0.5x?

Back

First, find g(6) = 4 - 0.5(6) = 1. Then, evaluate f(1) = 2(1)² - 10 = -8.

Front

What is the formula for the height of a projectile at time t?

Back

The height of a projectile can be modeled by the quadratic function h(t) = -0.5t² + vt + h₀, where v is the initial velocity and h₀ is the initial height.

Front

How do you find the value of a function at a specific point, such as f(3)?

Back

To find f(3), substitute 3 into the function: f(3) = 2(3)² - 10 = 8.