final exam alg 1 fall 24

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is given by the equation y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the slope of a line given two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What does the y-intercept represent in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of y when x = 0.

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, given by the formula x = -b/(2a) for a quadratic in the form y = ax^2 + bx + c.

Front

What is the vertex of a parabola in the form y = ax^2 + bx + c?

Back

The vertex can be found using the formula (-b/(2a), f(-b/(2a))) where f is the function.

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as x increases, y also increases, meaning the line rises from left to right.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as x increases, y decreases, meaning the line falls from left to right.

Front

What is the definition of a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically written in the form y = ax^2 + bx + c.

Front

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

Back

If the coefficient 'a' in the quadratic function y = ax^2 + bx + c is positive, it opens upwards; if 'a' is negative, it opens downwards.

Front

What is the formula for the vertex of the quadratic function y = ax^2 + bx + c?

Back

The vertex is given by the coordinates (-b/(2a), f(-b/(2a))).