Compare Quadratic Functions

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What does the y-intercept of a function represent?

Back

The y-intercept of a function is the point where the graph of the function crosses the y-axis, which occurs when x = 0.

Front

How can you determine the y-intercept from a quadratic equation?

Back

You can determine the y-intercept by substituting x = 0 into the quadratic equation, resulting in f(0) = c.

Front

What does it mean for a function to 'open up'?

Back

A quadratic function opens up if the coefficient 'a' in the standard form f(x) = ax² + bx + c is positive (a > 0).

Front

What is the vertex of a quadratic function?

Back

The vertex of a quadratic function is the highest or lowest point on the graph, depending on whether it opens up or down.

Front

How do you find the vertex of a quadratic function in standard form?

Back

The vertex can be found using the formula x = -b/(2a) to find the x-coordinate, and then substituting this value back into the function to find the y-coordinate.

Front

What is the significance of the outputs of a function at specific x-values?

Back

The outputs of a function at specific x-values indicate the corresponding y-values on the graph, showing the relationship between x and y.

Front

What does it mean if two functions have the same output for a given x-value?

Back

If two functions have the same output for a given x-value, it means that their graphs intersect at that point.

Front

What is the general shape of a quadratic function's graph?

Back

The graph of a quadratic function is a parabola, which can either open upwards or downwards.

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 equation x = -b/(2a).