2.4 Modeling with Quadratic Functions

Front

What is the vertex form of a quadratic function?

Back

The vertex form of a quadratic function is given by y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

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

Back

To find the vertex of a quadratic function in standard form y = ax² + bx + c, use the formula h = -b/(2a) and k = f(h).

Front

What does the 'a' value in the vertex form of a quadratic function indicate?

Back

The 'a' value determines the direction of the parabola (upward if a > 0, downward if a < 0) and the width of the parabola (narrower if |a| > 1, wider if |a| < 1).

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex represents the maximum or minimum point of the parabola, depending on the direction it opens.

Front

How can you determine if a set of data is quadratic?

Back

You can determine if a set of data is quadratic by checking if the second differences of the y-values are constant.

Front

What is the general form of a quadratic equation?

Back

The general form of a quadratic equation is y = ax² + bx + c.

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 = h, where h is the x-coordinate of the vertex.

Front

How do you convert a quadratic function from standard form to vertex form?

Back

To convert from standard form to vertex form, complete the square on the quadratic expression.

Front

What is the quadratic formula used for?

Back

The quadratic formula, x = (-b ± √(b² - 4ac)) / (2a), is used to find the roots (x-intercepts) of a quadratic equation.

Front

What is the relationship between the roots and the vertex of a quadratic function?

Back

The roots of a quadratic function are the x-values where the function equals zero, and the vertex is the midpoint of the roots if they are real and distinct.