(Alg.2) 4.1 (Flashcard) Quadratics Functions.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, represented as (h, k) in the vertex form of the equation y = a(x - h)² + k.

Front

How do you find the vertex of the quadratic function y = ax² + bx + c?

Back

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

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, found by setting y = 0 and solving for x.

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).

Front

What is the standard form of a quadratic function?

Back

The standard form is y = ax² + bx + c, where a, b, and c are constants.

Front

What is the vertex form of a quadratic function?

Back

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

Front

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

Back

If the coefficient 'a' in the standard form y = ax² + bx + c is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

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

Back

The 'a' value determines the width and direction of the parabola; larger absolute values of 'a' make the parabola narrower.

Front

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

Back

The y-intercept can be found by evaluating the function at x = 0, which gives the point (0, c) in the standard form.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of the quadratic equation ax² + bx + c = 0.