Algebra 1 2023 Midterm

Front

What is a system of equations with no solution?

Back

A system of equations with no solution occurs when the graphs of the equations are parallel lines, meaning they never intersect.

Front

How do you evaluate a quadratic function?

Back

To evaluate a quadratic function like f(x) = ax^2 + bx + c, substitute the value of x into the equation and simplify.

Front

If f(x) = 2x^2 - 4x, what is f(3)?

Back

f(3) = 2(3)^2 - 4(3) = 6.

Front

What does it mean for a quantity to vary directly with another?

Back

If a quantity varies directly with another, it means that as one quantity increases, the other quantity increases at a constant rate.

Front

If a car uses 6 gallons of gas for 180 miles, how many gallons does it use for 1,260 miles?

Back

42 gallons.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

How do you find the solution to an inequality like 4x + 1 ≥ 9?

Back

To solve 4x + 1 ≥ 9, subtract 1 from both sides, then divide by 4: x ≥ 2.

Front

What is a graph of a linear equation?

Back

A graph of a linear equation is a straight line that represents all the solutions of the equation.

Front

What does it mean for two lines to be parallel?

Back

Two lines are parallel if they have the same slope and will never intersect.