HW 2.1 Quadratic Functions

Front

What is a quadratic function?

Back

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

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is y = ax² + bx + c.

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on the direction it opens.

Front

How do you find the axis of symmetry for a quadratic function?

Back

The axis of symmetry can be found using the formula x = -b/(2a), where a and b are coefficients from the quadratic equation in standard form.

Front

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

Back

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

Front

What is the significance of the 'c' value in a quadratic function?

Back

The 'c' value represents the y-intercept of the quadratic function, which is the point where the graph intersects the y-axis.

Front

What is completing the square?

Back

Completing the square is a method used to convert a quadratic equation into a perfect square trinomial, making it easier to solve or graph.

Front

How do you complete the square for the expression p² + 14p?

Back

To complete the square, take half of the coefficient of p (which is 14), square it (49), and rewrite the expression as (p + 7)².

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is a quadratic expression that can be factored into the square of a binomial, such as (x + a)².

Front

How do you determine the value of 'c' to make x² + 8x + c a perfect square trinomial?

Back

To make x² + 8x + c a perfect square trinomial, set c equal to (8/2)², which is 16.