Algebra 1 Review

Front

What is a horizontal translation in graph transformations?

Back

A horizontal translation shifts the graph left or right without changing its shape. For example, g(x) = (x + 4)² is a horizontal translation of f(x) = x², moving it 4 units to the left.

Front

How do you solve a system of linear equations?

Back

To solve a system of linear equations, you can use substitution, elimination, or graphing methods to find the values of the variables that satisfy both equations.

Front

What does it mean if a system of linear equations has no solution?

Back

A system of linear equations has no solution if the lines represented by the equations are parallel and never intersect.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves. For the function f(x) = ax² + bx + c, the axis of symmetry can be found using the formula x = -b/(2a).

Front

What is the solution to the system of equations 3x + 2y = 16 and 7x + y = 19?

Back

The solution is (2, 5).

Front

What does it mean for two lines to intersect in a system of equations?

Back

If two lines intersect, it means there is a unique solution to the system of equations, represented by the point of intersection.

Front

What is a quadratic function?

Back

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

Front

How can you identify the vertex of a parabola?

Back

The vertex of a parabola represented by the equation f(x) = ax² + bx + c can be found using the formula (h, k) where h = -b/(2a) and k = f(h).

Front

What is the difference between a vertical and horizontal translation?

Back

A vertical translation shifts the graph up or down, while a horizontal translation shifts it left or right.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation of a system of equations consists of the lines or curves corresponding to each equation, and their intersection points represent the solutions.