Intro to Quadratic Functions

Front

What are the x-intercepts of a quadratic function?

Back

The x-intercepts are the points where the graph of the function crosses the x-axis, represented as (x, 0).

Front

What does the y-intercept of a quadratic function represent?

Back

The y-intercept represents the value of the function when x = 0, indicating the initial value of the function.

Front

Does a quadratic function have a maximum or minimum value?

Back

A quadratic function can have either a maximum or minimum value depending on the direction of the parabola (opening upwards or downwards).

Front

How do you find the y-intercept of a quadratic function?

Back

To find the y-intercept, substitute x = 0 into the function and solve for y.

Front

What is the range of a quadratic function that opens upwards?

Back

The range is all values of y greater than or equal to the minimum value.

Front

What is the standard form of a quadratic function?

Back

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

Front

What does the coefficient 'a' in a quadratic function indicate?

Back

The coefficient 'a' determines the direction of the parabola: if a > 0, it opens upwards; if a < 0, it opens downwards.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation.

Front

How can you determine if a quadratic function has real roots?

Back

You can determine this by calculating the discriminant (b^2 - 4ac); if it is positive, there are two real roots; if zero, one real root; if negative, no real roots.

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).