Algebra 1 EOC Review

Front

What is the average rate of change of a function?

Back

The average rate of change of a function over an interval is the change in the function's value divided by the change in the input value, calculated as \( \frac{f(b) - f(a)}{b - a} \) for the interval [a, b].

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 it opens.

Front

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

Back

A quadratic function \( f(x) = ax^2 + bx + c \) opens upwards if \( a > 0 \) and downwards if \( a < 0 \).

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is \( f(x) = ax^2 + bx + c \), where a, b, and c are constants.

Front

What is the formula for the vertex of a parabola given in standard form?

Back

The vertex of a parabola given by \( f(x) = ax^2 + bx + c \) can be found using the formula \( \left( -\frac{b}{2a}, f\left(-\frac{b}{2a}\right) \right) \).

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant \( D = b^2 - 4ac \) determines the nature of the roots of the quadratic equation: if \( D > 0 \), there are two distinct real roots; if \( D = 0 \), there is one real root; if \( D < 0 \), there are no real roots.

Front

What is a linear regression?

Back

Linear regression is a statistical method used to model the relationship between a dependent variable and one or more independent variables by fitting a linear equation to observed data.

Front

What is the formula for solving for a variable in an equation?

Back

To solve for a variable, isolate it on one side of the equation using inverse operations, such as addition, subtraction, multiplication, or division.

Front

What is the formula for the volume of a cone?

Back

The volume \( V \) of a cone is given by the formula \( V = \frac{1}{3} \pi r^2 h \), where \( r \) is the radius of the base and \( h \) is the height.

Front

How do you solve for height in the volume formula of a cone?

Back

To solve for height \( h \) in the volume formula \( V = \frac{1}{3} \pi r^2 h \), rearrange to get \( h = \frac{3V}{\pi r^2} \).